UNIVERSITY  OF  CALIFORNIA. 


(rl  FT     OK 


A  COURSE  OF  EXERCISES 


IN 


ELEMENTARY    PHYSICS. 


BY  HAROLD  WHITING,  PH.  D., 


Associate  Professor  of  Physics  in  the  University  of  California. 


PUBLISHED    BY 

THE    BERKELEY    PRESS, 

Box  2122, 

SAN  FEANCISCO, 
1894. 


COPYRIGHT  1894. 
By  HAROLD  WHITING. 


Table  of  Contents. 


HYDROSTATICS. 

*»1.    METRIC  AND  ENGLISH  MEASURES.      .        .        .        . 

**2.     DENSITY 3 

**3.    DISPLACEMENT.  5 

**4.     SPECIFIC  GRAVITY  BOTTLE.  *  7 

**5.    JOLLY  BALANCE. 9 

*6.    NICHOLSON'S  HYDROMETER.  10 

**7.    FLOTATION ...  11 

PRESSURE. 

**8.    BALANCING  COLUMNS 13 

*f9.     BAROMETER  AND  DALTON'S  LAW 16 

**10.     BOILING  AND  FREEZING-POINTS.         .-•'.'.        .        .        .  19 

*»11.    PRESSURE  OF  VAPORS.  21 

**12.     HYGROMETRY 23 

**13.    PNEUMATICS,    t 25 

EXPANSION. 

*U4.     EXPANSION  OF  LIQUIDS— BALANCING  COLUMNS.        .  27 

**15.    EXPANSION  OF  LIQUIDS— SPECIFIC  GRAVITY  BOTTLE.  29 

*16.    LINEAR  EXPANSION 31 

*17.    CHANGE  OF  VOLUME  IN  MELTING 33 

HEAT. 

**18.    LATENT  HEAT. 35 

**19.    SPECIFIC  HEAT-METHOD  OF  FUSION 37 

**20.    SPECIFIC  HEAT  OF  LIQUIDS ,     .  38 

**21.    MECHANICAL  EQUIVALENT  OF  HEAT.       ....  40 

$22.    ABSOLUTE  HEAT  CONDUCTIVITY 42 

*23.    RELATIVE  CONDUCTIVITY  AND  DIFFUSIVITY.     1        1  44 

**24.    RADIOMETRY.  .45 

LIGHT. 

**25.    RUMFORD'S  PHOTOMETER .47 

J26.    COLOR  PHOTOMETRY 49 

**27.     FOCI  OF  MIRRORS .51 

**28.    FOCI  OF  LENSES 53 

J29.    PHOTOGRAPHIC  CAMERA 55 

**30.    PHOTOGRAPHIC  PRINTING.      .......  58 

**31.     DRAWING  SPECTRA 60 

132.    DIFFRACTION. 61 

*Comparatively  elementary.  **Suitable  for  Preparatory  Schools, 

f  Difficult  of  explanation.  {Difficult  on  practical  grounds. 


IV  TABLE  OF  CONTENTS. 

SOUND. 

Page. 

**33.    CHLADNI'S  FIGURES 63 

**34.    NODES  OF  STRINGS  AND  PIPES.     .,.,..  65 

**35.    VIBRATION  OF  RODS.  ...,...,,  67 

*t36.    LISSAJOUS'   CURVES.             '        .  69 

*37.    LAWS  OF  STRINGS  AND  PIPES 70 

**38.    GRAPHICAL  MEASUREMENT  OF  PITCH.     .        .        .     .  .  71 

DYNAMICS. 

*39.    BREAKING  STRENGTH .73 

*40.    STRETCHING  WIRES .  75 

*41.     BENDING  BEAMS    .                                         77 

*42.    TWISTING  RODS 79 

*t43.    COUPLES 81 

*t44.    COMPOSITION  OF  FORCES 83 

*t45.    FALLING  BODIES 85 

MAGNETISM. 

U46.    MAGNETIC  ATTRACTIONS  AND  REPULSIONS.         .        .  88 

t47.    HORIZONTAL  COMPONENT  OF  THE  EARTH'S  FIELD.  .  92 

tJ48.    EARTH'S  ACTION  ON  SUSPENDED  MAGNET.   ...  95 

*}49.     EARTH'S  LINES  OF  FORCE 97 

**50.    MAPPING  MAGNETIC  FIELDS. 100 

ELECTROMAGNETISM. 

**51.    ELECTROMAGNETIC  RELATIONS 103 

*52.    LAWS  OF  ELECTROMAGNETIC  ATTRACTION.         .        .  106 

i    t53.    TESTING  AN  AMMETER 108 

ELECTRICAL    ENERGY. 

t54.    HEAT  AND  RESISTANCE .        .Ill 

**55.    DIVIDED  CIRCUITS 113 

**56.    ELECTRICAL  EFFICIENCY 115 

**57.     ELECTROCHEMICAL  RELATIONS 117 

*J58.    ARRANGEMENT  OF  BATTERIES 119 

*J59.    ELECTROMOTIVE  FORCE 121 

*J60.    OHM'S  LAW.               123 

tJ61.    FALL  OF  POTENTIAL  ALONG  A  CONDUCTOR.         .        .  125 

tt62.     ELECTRICAL  POWER 127 

MAGNETO-ELECTRIC  INDUCTION. 

tJ63.    MAGNETIO-ELECTRIC  INDUCTION 129 

tt64.    EARTH-INDUCTOR 131 

tJ65.    STUDY  OF  A  MOTOR  AND  DYNAMO-MACHINE.  133 


Comparatively  elementary.  **Suitable  for  Preparatory  Schools. 

fDifficult  of  explanation.  ^Difficult  on  practical  grounds. 


PREFACE. 


This  book  consists  in  a  collection  of  directions  for  some 
sixty  or  more  exercises  in  elementary  physics,  which  have 
been  given  during  the  current  academic  year  (1893 — 1894) 
to  students  in  the  University  of  California.  It  is  not  ex- 
pected that  these  directions,  which  were  prepared  under 
stress  of  work,  will  be  free  from  faults  or  inconsistencies; 
but  they  have  been  found  to  yield,  in  most  cases,  sufficiently 
satisfactory  results  to  warrant  their  issuance  for  another 
year;  and  it  has  been  thought  desirable  to  print  them — this 
being,  on  the  whole,  the  most  economical  method  of  distri- 
bution. 

A  secondary  object  in  printing  these  directions  has  been 
to  lay  before  the  teachers  of  this  State  a  proposed  line  of 
demarcation  between  High  School  and  College  work,  and  to 
invite  discussion  and  criticism  upon  this  subject.  The  ex- 
ercises included  in  this  book  are  not  intended  to  represent 
an  ideal  course  either  in  a  university  or  in  a  high  school; 
but  rather  a  collection  of  exercises  intermediate  in  grade  be- 
tween the  work  at  present  performed  in  high  schools,  and 
that  aimed  at  in  our  University.  The  desirability  of  a  com- 
plete understanding  and  accord  as  to  the  division  of  such 
work  between  School  and  College  must  be  evident  to  every 
teacher  of  physics  in  this  State. 

Excellent  suggestions  as  to  the  nature  of  a  High  School 
course  in  physics  will  be  found  in  the  report  of  two  mem- 
bers of  the  "Committee  of  Ten"  published  by  the  United 
States  Bureau  of  Education,  1893.  At  the  same  time, 


Tl  PREFACE. 

serious  faults  seem  to  exist  in  this  report.  The  introduction 
of  "Wheatstone's  bridge"  (before  the  student  has  any 
adequate  idea  of  the  distribution  of  potential  in  an  electric 
circuit)  is  certainly  objectionable;  as  is  also  the  study  of  the 
laws  of  motion  at  a  point  of  time  when  the  student  can 
hardly  be  familiar  with  the  mathematical  expressions 
necessary  to  the  understanding  of  acceleration.  On  the 
other  hand,  the  author  has  shown  that  a  determination  of 
the  "mechanical  equivalent  of  heat"  can  be  made  by  any 
student  with  considerable  accuracy  and  at  a  nominal  cost, 
as  far  as  apparatus  is  concerned.  Other  methods  of  reach- 
ing the  same  end  can  doubtless  be  devised  by  any  teacher 
having  a  moderate  degree  of  ingenuity.  Under  the  circum- 
stances, the  inclusion  of  this  fundamental  and  highly 
instructive  experiment  in  any  extended  high  school  course 
would  seem  to  be  desirable.  Several  other  criticisms  upon 
the  course  suggested  by  the  "Committee  of  Ten"  might  be 
made  here;  but  it  is  thought  that  the  author's  opinions  on 
this  subject  are  sufficiently  exemplified  by  the  list  of  exer- 
cises included  in  this  book. 

In  the  Table  of  Contents,  exercises  which  contain  parts 
suitable  (in  the  author's  opinion)  for  a  high  school  course 
are  marked  with  an  asterisk  (*),  and  those  which  might 
perhaps  be  adopted  without  essential  modification  are 
marked  with  two  asterisks.  Exercises,  however,  involving 
theoretical  difficulties,  which  cannot  be  explained  satis- 
factorily to  beginners,  are  distinguished  by  a  dagger  (t); 
and  those  offering  experimental  obstacles,  too  great  to  be 
overcome  in  the  teaching  of  large  classes,  are  distinguished 
by  a  double  dagger  (J). 

The  exercises  have  been  found  to  occupy  each  from  two 
to  three  hours  of  a  student's  time.  It  is  hoped  that  the 
majority  of  those  in  the  first  half  of  the  list  which  are 
doubly  starred  may  eventually  find  a  place  in  the  best  high 
schools,  without  prejudice  to  the  simpler  experiments  now 
taught  there.  In  order  that  a  place  may  be  found  for 
them,  it  is  suggested  that  certain  other  experiments  which 
have  been  found  to  offer  practical  or  theoretical  difficulties 


PREFACE.  Vll 

even  to  more  advanced  students  should  be  omitted.  The 
first  half  of  the  exercises  included  in  this  book,  covering 
hydrostatics,  heat,  light,  and  sound,  would  according  to 
this  scheme  fall  largely  to  the  High  School,  while  the  laws 
of  motion,  and  electrical  or  magnetic  measurements  in 
general,  would  constitute  a  more  advanced  course,  taught 
only  in  the  University,  or  in  schools  preparing  students  for 
advanced  standing. 

It  is  not  suggested  that  experiments  in  electricity  and' 
magnetism  should  be  excluded  altogether  from  the  High 
School,  but  that  the  work  in  these  branches  should  be  con- 
fined to  fundamental  phenomena,  and  that  these  even 
should  not  be  studied  to  the  prejudice  of  other  branches  of 
physics,  a  thorough  knowledge  of  which  is  necessary  for 
the  subsequent  understanding  of  the  phenomena  in 
question. 

Teachers  who  wish  to  introduce  exercises  like  those  here 
outlined  into  school  work  should  arrange,  if  possible,  to 
have  at  least  two  successive  school  hours  for  their 
laboratory  sections.  Each  student  should  be  assigned  to  a 
given  desk  (in  general)  for  a  given  day,  only.  He  should 
find  on  this  desk  all  the  apparatus  which  he  needs  (or  the 
materials  for  constructing  it),  together  with  notes  or  direc- 
tions supplementing,  when  necessary,  the  laboratory 
manual.  He  should  be  required  to  leave  his  desk  as  he 
found  it,  so  as  to  be  ready  for  the  student  next  behind  him 
in  order. 

The  apparatus,  if  there  is  not  a  complete  set  for  each 
member  of  a  given  section,  should  be  set  up  for  different  ex- 
periments on  different  desks,  in  so  far  as  may  be  practic- 
able, in  progressive  order,  so  that  a  whole  section  of 
students  may  be  moved,  at  the  proper  time,  each  from  one 
desk  to  the  next,  without  discontinuity,  in  the  case  of  any 
student,  in  the  course  of  experiments  followed.  Students 
working  more  slowly  than  others  should  be  allowed  more 
time  for  each  exercise,  or  required  to  make  up,  out  of 
hours,  for  what  they  have  lost,  so  as  to  be  ready  to  go  on 
with  their  work  without  losing  their  regular  places  in  their 


Vlll  PREFACE. 

section.  In  this  way  a  systematic  course  of  instruction  can 
be  given  to  large  sections,  with  a  very  limited  supply  of 
apparatus,  and  conflicts  in  the  use  of  this  apparatus  may  be 
avoided,  with  a  minimum  of  planning  on  the  part  of  the 
instructor. 

It  is  obvious  that,  in  following  any  systematic  course  of 
experiments  with  large  laboratory  sections,  supplied  with 
few  complete  sets  of  apparatus,  either  all  cannot  begin  and 
end  with  the  same  experiment,  or  else  some  must  enter  the 
course  later  than  others.  When  students  differ  greatly,  as 
is  generally  the  case  in  respect  to  intelligence  and  prepara- 
tion, it  may  be  desirable  to  start  them  with  different  exer- 
cises; but  in  the  most  unfavorable  case,  a  delay  of  two  or 
three  weeks  at  the  beginning  of  the  year  is  far  less  objec- 
tionable than  the  confusion  which  inevitably  results  from 
lack  of  sequence  in  experiments  like  those  outlined  in  this 
book. 

It  would  be  impossible  within  the  space  which  can  be  de- 
voted to  the  subject,  in  this  preface,  to  give  a  detailed 
description  of  the  system  of  instruction  recently  developed 
in  the  laboratories  at  Berkeley;  but  it  may  be  pointed  out 
that  farther  information  on  this  point  can  be  had  by  those 
attending  the  Summer  School  at  the  University,  or  by 
those  visiting  the  Physical  Laboratories.  The  author  will 
also  be  glad  to  answer  communications  addressed  to  him  on 
this  subject. 

The  exercises  in  this  book  have  been  developed  with  care 
to  avoid  calling  for  inferences  which  are  not  amply  justified 
by  the  data  before  the  student.  To  work  out  the  law,  for 
instance,  connecting  the  length  and  deflection  of  a  beam 
has  required  in  the  past  almost  numberless  experiments  on 
the  part  of  scientific  men.  A  single  pair  of  observations 
made  by  a  student  can  serve  at  the  most  to  enable  him  to 
select,  out  of  several  laws  suggested  to  him,  one  which 
satisfies  the  conditions  of  his  experiment.  One  of  the 
questions  on  this  exercise  is  put  to  the  student,  accordingly, 
in  this  form: —  IF  the  deflection  of  a  beam  is  proportional 
to  SOME  INTEGRAL  POWER  of  its  length,  what  is  the  power  in 


PREFACE.  IX 

question?  It  is  practically  easier  for  the  student  to  work 
this  out  by  experiment  than  to  look  it  up  in  a  text-book; 
and  by  not  telling  him  WHICH  power  to  expect,  some  point 
of  interest  is  given  to  his  work. 

Care  has  been  taken  in  so  far  as  possible  to  avoid  exer- 
cises which  can  serve  for  the  purpose  of  ILLUSTRATION  ONLY. 
If  an  experiment  is  "a  question  put  to  Nature,"  then  a  good 
experiment  is  one  which  enables  the  student  to  answer  one 
or  more  questions  that  he  could  not  answer  beforehand. 
Most  of  the  questions  appended  to  exercises  in  this  book 
have  been  found  by  practical  tests  to  be  of  this  nature.  It 
is  though  that  similar  tests  should  be  applied  to  experi- 
ments performed  in  the  schools.  When  students  are  unable, 
after  performing  an  exercise,  to  answer  the  questions  which 
it  is  intended  to  illustrate,  the  exercise  has  been  useless  as 
far  as  they  are  concerned.  If,  on  the  other  hand,  they  are 
able  to  answer  these  questions  beforehand,  the  exercise  is 
needless,  and  they  should  be  allowed  to  substitute  some 
other  piece  of  work. 


The  author  is  indebted  to  Mr.  E.  R.  Drew,  instructor  in 
physics  in  this  University,  for  valuable  aid  in  the  prepara- 
tion of  the  course  of  exercises  here  outlined,  and  for  re- 
vision of  the  manuscript.  Thanks  are  also  due  to  every 
member  of  the  Physical  Department  for  numerous  sug- 
gestions and  hearty  cooperation  in  the  development  of  the 
course.  In  the  expectation  of  revising  or  reprinting  these 
directions  for  exercises  in  physics  from  year  to  year,  sug- 
gestions from  all  sources  will  be  gladly  received. 

HAROLD  WHITING. 
BERKELEY,  CALIFORNIA,  May  1st,  1894 


EXERCISES 


IN 


ELEMENTARY    PHYSICS. 


1.    METKIC  AND  ENGLISH  MEASUEES. 

APPAKATUS  :  A  set  of  Avoirdupois  weights,  a  set  of  Metric 
weights,  (to  1  d.  g.);  trip  scales;  two  metre  rods  in  inches 
and  in  mm.  A  spring  balance  graduated  in  decimal  multi- 
ples of  a  dyne. 

I.  Find  the  weight  in  grams  of  several  avoirdupois  stan- 
dards.      Adjust  to  0.  1  gram  in  each  case.        Calculate  the 
value  of  the  pound,  ounce,  and  grain  in  grams.     Retain  four 
figures  in  each  result. 

If  the  results  of  weighing  the  different  standards  do  not 
agree,  select  the  best  as  a  basis  for  your  calculations,  or  if 
two  or  more  weighings  seem  equally  reliable,  average  the 
results.  Why  do  you  prefer  a  weighing  with  large  weights 
to  one  with  small  weights? 

Would  the  results  of  weighing  be  affected  by  an  increase 
or  diminution  in  the  earth's  attraction  for  the  bodies  in 
question?  Give  reasons  for  your  answer. 

II.  Lay  a  metre  rod  graduated  in  millimetres  beside  one 
graduated  in  inches  and  eighths,   so  that  the   two   scales 
meet.       Make  the  5-inch  division  coincide  with  the  127th 
mm.  division.       What  other  inch  divisions  coincide  exactly 
with  the  mm.  divisions  next  to  them?     and  with  what  mm. 


2  METRIC  AND   ENGLISH  MEASURES.  [1 

divisions  do  they  each  coincide?  Calculate  from  several  of 
these  data  the  value  of  the  inch  in  millimetres.  Carry  out 
your  work  to  three  places  of  decimals.  Why  do  you  prefer 
to  base  your  calculation  on  a  comparison  involving  a  large 
number  of  inches  and  millimetres? 

III.  Why  is  it  unnecessary  to  make  a  comparison  of  the 
units  of  time  employed  in  the  Metric  and  English  systems? 

IV.  Find,  by   suspension  from   a    spring    balance,  the 
weight    in    dynes,  of   several  Avoirdupois   standards,  also 
that  of  several  Metric  standards  of  mass. 

Calculate  the  weight  of  one  gram  in  dynes.  How  would 
this  be  affected  (if  at  all)  by  an  increase  or  diminution  in  the 
earth's  gravity  ?  (ask  if  you  do  know.) 

What  kind  of  instrument  would  you  use  to  find  the  mass 
(or  weight  in  grams)  of  a  body,  and  what  kind  of  instrument 
would  you  employ  for  a  measurement  of  the  weight  in 
dynes  of  (or  force  exerted  by  gravity  upon)  a  body  ?  and 
why? 

Give  some  idea  of  a  numerical  measure  of  the  earth's 
gravity  suggested  by  your  observations. 


2]  DENSITY. 


2.    DENSITY. 

APPARATUS  :  A  wooden  block,  1  decim.  cube  ;  a  similar 
block  loaded  with  shot ;  a  mould  to  fit  the  same  ;  a  hollow 
decim.  cube  ;  scales  and  weights  to  1  gram ;  a  vessel  with 
shot  for  counterpoising ;  a  metre  rod ;  a  pail  for  water ;  a 
mop  cloth  ;  access  to  a  vernier  gauge,to  an  air-pump,  and  to 
supplies  of  water,  coal-oil  and  gas. 

I.  Find  the  length,  breadth  and  thickness  of  the  block 
of  wood  by  the  vernier  scale.     If  the  measurements  of  a 
given  dimension  differ,  record  the  mean  (or  average).       Ask 
for  instructions  (if  necessary)  as  to  the  use  of  the  vernier 
scale.     Weigh  the  block  on  the  balance  to  one  gram.       Cal- 
culate the  surface  of  the  block  in  square  centimetres,  its 
volume  in  cubic  centimetres,  and  its  density  in  grams  per 
cubic  centimetre. 

II.  Repeat  I.  with  a  hollow  block,  loaded  with  shot,  so 
as  neither  to  rise  nor  sink  when  immersed  in  water. 

NOTE.  If  the  loaded  block  and  the  solid  block  both  fit 
the  same  mould,  the  measurements  of  length,  breadth  and 
thickness  in  I.  need  not  be  repeated. 

III.  Find  the  inside  measurements  of  the  rectangular 
mould. 

NOTE.  If  the  block  fits  the  mould,  the  measurements  of 
the  block  may  be  taken  for  those  of  the  mould. 

Place  the  mould  on  the  balance,  counterpoise  it  with 
shot,  fill  with  water  by  means  of  a  small  beaker,  and  find 
the  weight  of  the  water  within  one  gram. 

Calculate  the  density  of  the  water  to  three  decimal 
places.  (Eepeat  until  the  result  lies  between  .990  and 
1.020).  "What  relation  exists  between  the  density  of  water 
and  that  of  a  loaded  block  (see  II.)  which  neither  rises  nor 
sinks  in  the  water? 


4:  DENSITY.  [2 

Dip  some  of  the  water  out  of  the  mould  by  means  of  the 
small  beaker,  held  lip  downward  while  being  lowered,  so  as 
not  to  cause  overflow.  Then  pour  away  the  rest  of  the 
water,  and  dry  the  mould  with  a  cloth. 

IV.  Kepeat  III.  with  coal-oil  instead  of  water.       Calcu- 
late the  density  of  the  coal-oil,  and  also  its  relative  density 
or  specific  gravity  referred  to  water,  calling  the  density  of 
water  0.998. 

V.  Find  roughly  the  capacity  of  a  hollow  brass  cube  by 
outside  measurements,  allowing,  as  well  as  may  be,  for  the 
thickness  of  the  brass. 

Counterpoise,  approximately,  by  lead  shot. 

Exhaust  as  much  air  as  possible  by  the  air-pump. 
(About  20  strokes  will  do). 

Counterpoise,  again,  only  more  exactly,  with  lead  shot, 
noticing  whether  the  cube  has  gained  or  lost  in  weight. 

Exhaust  with  the  air-pump  until  the  weight  becomes  con- 
stant. This  is  shown  by  the  agreement  of  two  successive 
weighings. 

Admit    air,   and    find  the  gain  in    weight    within    ONE 

DECIGRAM. 

Calculate  the  density  of  the  air. 

VI.  Pass  a  current  of   coal-gas  through  the  cube  until 
the  lighted  jet  shows  a  white  flame.      Find  the  difference  of 
the  weights  of  the  cube  with  coal-gas  and  with  air  within 

ONE  DECIGRAM. 

Calculate  the  density  of  the  coal-gas,  also  its  specific 
gravity  referred  to  air  of  the  same  temperature. 


3]  DISPLACEMENT.  5 


3.    DISPLACEMENT. 

APPARATUS  :  A  glass  ball,  a  wire  cage  for  ditto. ;  an  over- 
flow beaker ;  a  ring  stand ;  a  4  oz.  beaker ;  a  vessel  with 
shot  for  counterpoising ;  scales  and  weights ;  water  and 
coal-oil. 

I.  Weigh  the  glass  ball  to  a  gram.       Fill  the  overflow- 
beaker  with  water  until  it  runs  out  of  the  spout,  and  catch 
the  overflow  in  a  smaller  beaker.       Empty  this  beaker,  and 
counterpoise  it  with  shot.         Replace  it  beneath  the  spout. 
Lower  the  ball  in  its  cage  into   the   overflow-beaker,  and 
catch  the  overflow.          Eeplace  the  beaker  on  the  scales,  to 
find  the   weight  of  the  overflow.       Answer  the    following 
questions : 

What  takes  place  when  the  ball  is  lowered  into  the  over- 
flow-beaker? How  can  you  find  the  weight  of  the  water 
displaced  by  a  body,  (i.  e.  the  weight  of  an  equal  bulk  of 
water)? 

How  should  the  experiment  be  modified  so  that  the 
weight  of  water  displaced  by  the  wire  cage  may  not  be 
added  to  that  displaced  by  the  ball  ? 

Find  the  specific  gravity  of  the  glass  ball  by  this 
experiment 

II.  Hang  up  the  glass  ball  on  a  stand  resting  on  one  pan 
of  the  balance,  counterpoise  it  with  lead  shot,  and  then  sur- 
round it  with  water  in  a  beaker  supported  by  the  hand,  so 
as  not  to  touch  the  ball.     Add  weights  to  the  lighter  side  of 
the  balance  until  equilibrium  is  restored. 

Does  the  ball  gain  or  lose  in  weight  when  thus  immersed 
in  water? 

Does  the  gain  or  loss  of  weight  appear  to  be  much  greater, 
much  less,  or  about  the  same  as  the  weight  of  water  dis- 
placed by  the  ball  in  I.  ?  How  could  the  effect  of  the  cage 
be  eliminated? 


6  DISPLACEMENT.  [3 

Find  the  specific  gravity  of  a  ball  by  the  method  in  II., 
combined  with  the  weighing  of  the  ball  in  I. 

III.  Place  a  beaker  half-filled  with  water  on  the  scales. 
Counterpoise  it  with  lead  shot.  Lower  the  glass  ball  into 
the  water  so  as  to  be  completely  immersed,  but  not  to  touch 
the  sides  or  bottom  of  the  beaker.  Add  weights  to  produce 
equilibrium. 

Does  the  beaker  gain  or  lose  in  weight  when  the  ball  is 
lowered  into  it  ? 

What  relation  exists  between  the  gain  and  loss  of  weight 
and  other  quantities  previously  determined? 

Find  the  specific  gravity  of  the  ball  by  the  data  in  III. 
combined  with  the  weight  of  the  ball. 

How  should  the  method  in  III.  be  modified  so  as  to  elimi- 
nate the  effect  of  the  wire  cage? 

Which  of  the  three  methods  seems  to  you  the  best,  in  view 
of  the  simplicity  of  apparatus,  universal  applicability,  and 
accuracy  of  results  ? 

IY.  Kepeat  I.,  II.,  and  III.,  if  time  permits,  with  coal-oil 
instead  of  water,  and  calculate  the  specific  gravity  of  the 
coal-oil  from  the  results  of  each  method,  instead  of  calcu- 
lating the  specific  gravity  of  the  ball. 


4]  SPECIFIC  GRAVITY  BOTTLE. 


4.   SPECIFIC  GKAVITY  BOTTLE. 

APPARATUS  :  An  8-oz.  wide  mouth  bottle  with  solid  glass 
stopper ;  scales  with  weight  from  1  kilo,  to  1  decigram ;  a 
vessel  with  lead  shot  for  counterpoising;  sand,  salt,  water 
and  coal-oil ;  a  drying  cloth. 

NOTE.  Always  weigh  the  bottle  WITH  the  stopper,  or 
counterpoise  it  WITH  the  stopper.  Keep  the  outside  of  the 
bottle  clean  and  dry.  Dry  the  inside  of  the  bottle  with 
cotton  waste  after  weighing  with  liquid.  In  putting  the 
stopper  in  place  when  the  bottle  contains  liquid,  tip  the 
bottle  and  stopper  one  side,  so  as  to  allow  air-bubbles  to 
escape. 

I.  Counterpoise  the  bottle  with  shot,  fill  with  water,  and 
find  the  weight  of  the  water. 

Calculate  the  capacity  of  the  bottle  in  cubic  centimetres, 
allowing  1.002  cu.  cm.  to  the  gram. 

II.  Eepeat  I.  with  coal-oil  instead  of  water.       Calculate 
the  specific  gravity  of  the  coal-oil. 

III.  Nearly  fill  the  bottle  with  sand,  and  find  the  weight 
of  the   sand  in  the  bottle.      (This  is  more  accurate  than 
weighing  the  sand  separately,  on  account  of  the  danger  of 
spilling). 

IV.  Counterpoise   the   bottle   containing  the   sand,   by 
means  of  lead  shot.       Fill  the  spaces  between  the  particles 
of  sand,  and  above  the  sand,  with  water ;  and  shake  the  con- 
tents once  or  twice  so  as  to  free  bubbles  of  air.        Find  the 
weight  of  the  water  necessary  to  fill  that  part  of  the  bottle 
which  is  not  occupied  by  the  sand. 

Why  is  the  weight  of  water  in  the  bottle  less  in  IV.  than 
in  I? 

How  can  you  find  the  weight  of  water  displaced  by  the 
sand? 


8  SPECIFIC  GRAVITY  BOTTLE.  [4 

Calculate  the  specific  gravity  of  the  sand. 

V.  Dry  the  bottle  carefully,  and  repeat  III.  with  common 
salt,  or  any  salt  soluble  in  water. 

VI.  Eepeat  IV.  with  the  salt  in  V.  instead  of  sand,  and 
with  coal-oil  instead  of  water. 

Why  could  not  water  be  used  in  VI.  as  in  IV,  instead  of 
coal-oil  ? 

Find  the  weight  of  coal-oil  displaced  by  the  salt,  also  the 
specific  gravity  of  the  salt  referred  to  the  coal-oil. 

Knowing  the  specific  gravity  of  coal-oil,  from  II.,  how  can 
you  find  the  weight  of  an  equal  bulk  of  water  ? 

Calculate  the  specific  gravity  of  the  salt  from  its  weight 
as  compared  with  that  of  an  equal  bulk  of  water. 

What  is  the  algebraic  relation  between  (a)  the  specific 
gravity  of  salt  referred  to  coal-oil,  (b)  the  specific  gravity 
of  coal-oil  referred  to  water  and  (c)  the  specific  gravity  of 
salt  referred  to  water? 


5]  JOLLY    BALANCE.  9 


5.    JOLLY  BALANCE. 

APPARATUS  :  A  Jolly  balance,  (including  beaker  and  metre 
rod),  with  weights  from  1  to  5  grams ;  pieces  of  glass  weigh- 
ing BETWEEN  3  and  4  or  between  4  and  5  grams  ;  water  and 
coal-oil. 

I.  Fill  the  beaker  with  water,  place  it  on  the  adjustable 
shelf,  and  raise  or  lower  the  shelf  until  the  lower  pan  and  a 
definite  portion  of  the  wire  by  which  it  is  suspended  are  im- 
mersed. ALWAYS  ADJUST  IN  THIS  WAY,  whether  a  weighing  is 
to  be  made  in  air  or  in  water. 

Eead  the  balance  by  the  horizontal  ring,  holding  the  eye 
so  that  the  nearer  and  farther  limits  of  the  ring  coincide  in 
direction — in  other  words,  sighting  along  the  plane  of  the 
ring.  Estimate  if  possible  the  tenths  of  millimetres  indi- 
cated upon  the  vertical  scale  of  mm. 

Repeat  the  reading  with  1,  2,  3,  4,  and  5  grams  in  the 
upper  pan.  Do  not  weigh  objects  heavier  than  5  grams, 
lest  the  elastic  limits  of  the  spring  should  be  exceeded. 

Eead  again  with  a  small  piece  of  glass  in  the  upper  pan. 

Eead  again  with  the  piece  of  glass  in  the  lower  pan. 

Calculate  by  interpolation  the  weight  in  grams  of  the 
glass  in  air,  and  in  water;  also  the  specific  gravity  of  the 
glass  referred  to  the  water. 


II.  Eepeat  I.  with  coal-oil  instead  of  water,  only  instead 
of  calculating  the  specific  gravity  of  the  glass  referred  to 
the  coal-oil,  calculate  that  of  the  coal-oil  referred  to  water. 


10  NICHOLSON'S  HYDROMETER.  [6 


6.    NICHOLSON'S  HYDROMETER. 

APPARATUS  :  A  Nicholson's  hydrometer,  with  jar  and  with 
weights  from  20  grams  to  1  centigram ;  two  small  objects, 
one  denser,  the  other  less  dense  than  water. 

I.  Find  the  weight  necessary  to  sink  the  Nicholson's  hy- 
drometer to  a  given  mark  on  the  stem,  one  or  two  cm.  above 
the  body  of  the  instrument.     Take  care  to  keep  the  weights 
dry.     See  that  the  water  is  not  deep  enough  to  allow  the 
upper  pan  to  be  submerged.        Keep  the  hydrometer  in  the 
middle  of  the  jar,  to  avoid  friction.     Adjust  the  weights  to  1 
centigram. 

II.  Repeat  I.  with  a  marble  in  the  upper  pan.      Why 
does  it  take  less  weight  than  before  to  sink  the  instrument 
to  the  mark?      Calculate  the  weight  of  the  marble  from  the 
data  already  obtained. 

III.  Repeat  II.  with  the  marble  in  the  lower  pan.     Is 
the  weight  required  to  sink  the  instrument  greater  or  less 
than  when  the  marble  was  in  the  upper  pan?     and  why? 
Calculate  the  weight  of  the  marble   in  water,   its  loss   of 
weight  in  water,  the  weight  of  a  quantity  of  water  equal  to 
the  marble  in  bulk,  and  the  specific  gravity  of  the  marble 
referred  to  the  water. 

IV.  Eepeat  II.-III.   with  a  piece  of  cork  instead  of  a 
marble.     Suspend  the  lower  pan  upside  down,  and  place  the 
cork  beneath  it  in  weighing  in  water. 

Is  the  weight  of  the  cork  in  water  positive  or  negative  ? 
Is  the  weight  of  water  displaced  by  the  cork  the  numerical 
or  the  algebraic  difference  between  the  weights  of  the  cork 
in  air  and  in  water  ?  Find  the  specific  gravity  of  the  cork 
referred  to  the  water. 

V.  Reweigh  the  cork,  as  in  II. 

Does  the  cork  gain  in  weight  during  these  experiments, 
and  why?  How  would  you  avoid  possible  errors  from  this 
source  ? 


7]  FLOTATION. 


7.    FLOTATION. 

APPAKATUS  :  A  hydrometer  jar,  a  strip  of  wood,  a  specific 
volumenometer,  a  universal  hydrometer;  water,  alcohol, 
coal-oil,  saline  solution,  salt,  dilute  sulphuric  acid ;  a  glass 
tunnel. 

I.  Place   a   strip  of  wood  (similar  to  the   wood  of  the 
block  in  Exp.  2,)  in  a  hydrometer  jar,  and  fill  the  jar  with 
water.      Mark  the  water-level  in  pencil  on  the  strip.      Find 
the  length  of  the  strip,  and  the  length  of  the  portion  im- 
mersed. 

Calculate  the  specific  gravity  of  the  strip  referred  to  the 
water.  How  does  this  compare  with  the  results  obtained 
with  the  same  wood  in  Exp.  2? 

II.  Kepeat  I.  with  coal-oil  instead  of  water.        Does  the 
strip  float  at  the  same  or  at  a  different  depth  and  why? 
Calculate  the  specific  gravity  of  the  coal-oil  referred  to  the 
water. 

III.  Float  a  hydrometer   showing  "specific  volumes"  in 
water,  and  note  the  reading. 

What  practical  advantages  are  possessed  by  this  instru- 
ment over  the  crude  form  of  hydrometer  used  in  I.  and  II.  ? 

IY.  Eepeat  III.  with  dilute  sulphuric  acid  instead  of 
water. 

Calculate  the  specific  gravity  of  the  acid. 

Y.  Find  the  readings  of  a  "Universal  Hydrometer"  in 
water,  in  coal-oil,  and  in  acid. 

How  do  these  readings  compare  with  the  specific  gravities 
of  those  liquids  already  found  ? 

What  advantage  is  possessed  by  a"Universal  Hydrometer" 
for  the  rapid  determination  of  specific  gravities? 

YI.     Make  a  ten  per  cent,  solution  of  common  salt,  (50 


12  FLOTATION.  [7 

grams  salt,  450  grams  water),  and  find  its  specific  gravity 
by  the  "Universal  Hydrometer." 

VII.  Find  the  specific  gravity  of  a  saline  solution  of  un- 
known strength. 

Is  the  strength  of  the  solution  greater  or  less  than  ten 
per  cent.  ?  and  why  ? 

Make  a  rough  estimate  of  the  strength  of  the  unknown 
solution. 

VIII.  Find  the  strength  of  a  mixture  of  alcohol  and 
water  by  the  following  table  showing  per  cents,  by  weight 
and  specific  gravities  at  about  20°  C. 

0123456789 

0    .998    996  994    993    991    989    988    986    984    983 

10     982    980  978    977    976    975    974    972    971    970 

20     969    967  966    965    964    962    961    959    958    956 

30     954    953  951    949    947    945    943    941    939    938 

40     935    933  931    929    927    925    923    921    918    916 

50     914    912  910    907    905    903    901    898    896    894 

60     891    889  887    884    882    880    877    875    873    870 

70     868    866  863    861    858    856    853    851    849    846 

80     844    841  839    836    834    831    829    826    823    821 

90     818    815  813    810    807    805    802    799    796    793 

100     790 

[The  first   line  in  this  table  contains  the  specific  gravity 

of  alcohol  from  0%  to  9%;  the  second  line  from  10%  to 

19%,  etc.,  etc.] 


8]  BALANCING    COLUMNS.  13 


8.    BALANCING  COLUMNS. 

APPARATUS  :  A  metre  rod ;  a  beam  compass ;  a  U-tube,  a 
W-tube,  and  a  Y-tube  (with  two  beakers);  mercury,  water, 
coal-oil,  alcohol,  and  one  or  more  other  liquids ;  a  glass 
tunnel ;  a  piece  of  fine  wire  with  swab ;  a  slop  jar ;  3  burette 
stands  to  support  tubes. 

NOTE.  The  balancing  columns  throughout  this  experi- 
ment are  supposed  to  be  vertical. 

I.  Pour  some  mercury  (through  a  tunnel)  into  a  glass  U- 
tube,  until  it  stands  about  5  cm.  deep  in  both  arms  of  the 
"U,"  then  fill  the  longer  arm  of  the  U-tube  with  water  until 
the  water  stands  about  13.6  cm.  deep.     Work  out  all  air- 
bubbles,  if  necessary,  with  a  fine  wire.     Measure  the  length 
of  the  column  of  water,  and  the  height  of  each  end  of  the 
U-shaped  column  of  mercury  above  the  table. 

Does  the  mercury  stand  at  the  same  level  as  the  water  or 
not  ?  and  why  ? 

What  differences  do  you  notice  between  the  shapes  of  the 
free  ends  of  the  two  columns? 

II.  Pour  a  little  more  mercury  into  the  shorter  arm  of 
the  U-tube,  so  as  to  raise   the  level  about  5  cm.     Repeat 
measurements  as  in  I. 

Is  the  length  of  the  column  of  water  altered  by  the  addi- 
tion of  the  mercury,  or  is  the  column  of  water  simply  pushed 
higher  up  in  the  tube  ? 

Find  by  appropriate  measurements  the  length  of  the 
column  of  mercury  which  balances  the  column  of  water  both 
in  I.  and  in  II. 

III.  Fill  up  the  longer  arm  of  the  U-tube  with  water, 
until  it  comes  within  5  or  10  cm.  of  the   top  of  the  tube. 
Find  the  length  of  the  column  of  water,   and   that  of  the 
column  of  mercury  which  balances  it. 


14  BALANCING  COLUMNS.  [8 

Calculate  the  specific  gravity  of  the  mercury  referred  to 
the  water. 

IV.  Empty  the  contents  of  the  tube  in  III.  into  a  jar, 
and  balance,  as  in  III.,  a  column  of  coal-oil  with  one  of 
water. 

Which  liquid  should  be  poured  in  first  ?  and  which  should 
occupy  the  longer  arm  of  the  U-tube? 

Calculate  the  specific  gravity  of  the  coal-oil  by  the  prin- 
ciples already  worked  out.  Does  this  correspond  as  nearly 
as  might  be  expected  with  the  results  of  previous  experi- 
ments with  coal-oil  ? 

Y.  Why  cannot  the  U-tube  already  employed'  be  used  to 
find  the  specific  gravity  of  liquids  which  mix  with  water  ? 

Point  out  the  obvious  advantages  of  a  W-tube  for  this 
purpose. 

If  the  middle  part  of  the  W-tube  is  not  very  high,  why 
must  the  balancing  columns  be  added  alternately,  little  by 
little,  instead  of  all  at  once,  as  in  IV.? 

Balance  a  column  of  water  against  one  of  alcohol  (or  one 
of  ammonia)  in  a  W-tube,  paying  attention  to  the  precaution 
above. 

Why  does  each  liquid  stand  at  two  different  levels  in  its 
own  branch  of  the  "W?" 

Find  by  the  appropriate  measurements,  the  length  of  the 
two  balancing  columns.  (State  how  you  do  this). 

Calculate  the  specific  gravity  of  the  alcohol  (or  the 
ammonia). 

VI.  Fill  one  beaker  nearly  full  with  water,  and  another 
beaker  with  some  saline  solution.  Place  the  feet  of  an  in- 
verted Y-tube,  one  in  each  beaker.  Raise  both  liquids  as 
far  as  may  be  safe  or  practicable  by  suction  through  the 
stem  of  the  "Y,"  and  close  this  stem  air-tight. 

Why  does  each  liquid  stand  higher  in  its  own  branch  of 
the  "T  "  than  in  the  beaker  ? 

Find  by  appropriate  measurements  the  lengths  of  the  two 
balancing  columns.  (State  how  you  do  this). 

Calculate  the  specific  gravity  of  the  saline  solution. 


8]  BALANCING    COLUMNS.  15 

VII.  Which  of  the  three  methods  above  (IV.,  V.,  or  VI.) 
is  preferable  in  the  case  of  liquids  which  do  not  mix?  in  the 
case  of  liquids  which  mix,  but  are  not  volatile  or  hygro- 
scopic? in  the  case  of  other  liquids?  Which  is  the  most 
general  method  of  balancing  columns? 

Find  as  in  IV.,  V.,  or  VI.  the  specific  gravity  of  other 
liquids,  if  time  permits,  using  the  appropriate  method  in 
each  case. 


16  BAROMETER  AND  DALTON'S  LAW.  [9 


9.    BAEOMETEK  AND  DALTON'S  LAW. 

APPARATUS  :  A  barometer-tube,  medicine-dropper  ;  a 
small  glass  tunnel ;  a  150-gram  bottle  with  rubber  stopper 
perforated  by  glass  tube;  a  rubber  bulb  with  connecting 
tube;  a  wire  with  swab ;  a  burette  stand ;  mercury  and  ether ; 
a  metre  rod. 

I.  Take  a  barometer-tube  at  least  80  cm.  long,  carefully 
clean  and  dry  it  by  a  wad  of  cotton  on  the  end  of  a  wire. 
Pour   in  mercury   little   by    little,   from    a  small  beaker, 
through  a  tunnel,  until  the  tube  is  nearly  full.     Close  the 
open  end  of  the  tube  with  the   finger,  and  invert  several 
times,  so  as  to  collect  all  air-bubbles  into  one,  then  fill  com- 
pletely with  mercury.      Place  the  finger  once  more  over  the 
end  of  the  tube,  invert  the  tube ;  immerse  the  open  end  in  a 
small  cistern  containing  mercury  at  least  2  cm.  deep,  then 
remove  the  finger.     What  does  the  mercury  do? 

II.  Keplace  the  finger  beneath  the  open  end  of  the  tube 
while  under  the  mercury  in  the  cistern.     Invert  the  tube 
several  times,  so  as  to  "rinse  it  out  with  the  partial  vacuum" 
which  it  now  contains,  then  fill  up  again  with  mercury,  close 
the  end  with  the  finger,  invert,  and  open  under  the  mercury 
in  the  cistern  as  before. 

III.  Tip  the  tube  sideways  until  the  top  is  not  more  than 
70  cm.  higher  than  the  cistern.     Does  the  mercury  com- 
pletely fill  the  tube?  or  is  there  an  air-bubble  above  the 
mercury?       Repeat  II.  until  all  traces  of  an  air-bubble  dis- 
appear, or  until  the  size  of  the  air-bubble  is  reduced  to  a 
minimum.       What  kind  of  a  sound  does  the  mercury  now 
make  when  it  strikes  the  top  of  the  tube  ?       (Be  careful  not 
to  let  it  strike  too  hard). 

IV.  Find  the  vertical  height  of  the  column  of  mercury 
above  the  level  of  the  mercury  in  the  cistern.  What  balances 


9]  BAROMETER  AND  DALTON'S  LAW.  17 

this   column  of  mercury?     What  is  meant  by  barometric 
pressure? 

V.  Fill  a  medicine-dropper  completely  with  ether,  and 
inject  a  few  drops  into  the  open  end  of  the  barometer  be- 
neath the  mercury  in  the  cistern.      Take  care  not  to  let  any 
air  in.     Describe  in  detail  what  takes  place.      Find  the  new 
height  of  the  barometric  column.     "Why  is  this  less  than 
before  ?     Calculate  the  fall  of  the  barometric  column  caused 
by  the  admission  of  ether.         Find  the  pressure  (in  cm.  of 
mercury)  of  ether  vapor  in  a  vacuum,  at  the  temperature  of 
the  room. 

VI.  Pour  some  mercury,  to  a  depth  of  2  or  3  cm.,  into  a 
150-gram  bottle,  carefully  cleaned  and  dried.     Insert  a  glass 
tube,  at  least  50  cm.  long,  through  a  rubber  stopper,  so  as 
to  reach  the  bottom  of  the  bottle.     Take  care  that  the  stop- 
per is  air  tight.     Measure  the  height  (if  any)  of  the  mercury 
in  the  tube  above  its  level  in  the  bottle.      Pour  some  ether 
into  the  open  end  of  the  tube,  until  it  stands  in  an  unbroken 
column  30  or  40  cm.  deep.     (Air-bubbles  can  be  worked  out 
if  necessary  by  a  wire).     Measure  the  height  of  the  ether 
column.     Attach  a  rubber  bulb  to  the  open  end  of  the  tube, 
and  force  a  little  ether  into  the  bottle.     Be  careful  not  to 
force  in   any   air.     What  is  the  effect  of  introducing  the 
ether  ?* 

VII.  FORCE  IN  MORE  ether,  until  the  top  of  the  ether 
column  stands  at  its  ORIGINAL  height,  in  VI.      How  does  the 
volume  of  the  air  in  the  flask  now  compare  with  its  original 
volume  before  the  introduction  of  the  ether?     And  how  does 
the   pressure   within  the   flask   compare   with  its  original 
pressure?     Does  all  the  ether  evaporate?     Or  does  it  cease 
to   evaporate  after  a  certain  amount  has  been  introduced? 
What  is  the  effect  of  saturating  a  given  volumn  of  air  with 
ether  vapor? 

VIII.  Measure  the  height  of  the  column  of  mercury  in 
the   tube   above   that  in  the  bottle.     Find  the  increase  of 
pressure  within  the  flask  over  its  pressure  in  VI.,  before  the 

*This  method  of  introducing  ether  into  a  manometer  is  due  to  Mr.  Thorpe. 
2 


18  BAROMETER  AND  DALTON'S  LAW.  [9 

introduction  of  ether.  How  does  this  increase  of  pressure 
compare  with  the  pressure  produced  by  the  vapor  of  ether 
in  a  vacuum  ?  (see  V.) 

Repeat  V.,  VI.  and  VII.  until  you  feel  sure  of  your 
last  answer. 

Are  the  pressures  due  to  a  given  vapor  at  a  given  temper- 
ature approximately  equal,  whether  produced  in  a  vacuum 
or  in  the  presence  of  a  gas?  or  do  these  pressures  differ  by 
an  amount  considerably  greater  than  the  probable  error  of 
observation? 

Note  that  a  correct  answer  to  the  last  question  is  equiva- 
lent to  "DALTON'S  LAW". 


10]  BOILINQ  AND  FREEZING-POINTS.  19 


10.    BOILING  AND  FKEEZING-POINTS. 

APPARATUS  :  200  grains  of  ice,  with  a  hammer  and  cloth 
for  powdering  the  same ;  a  dish  to  melt  paraffine,  an  alcohol 
lamp,  a  beaker,  two  test-tubes  (one  large,  the  other  small); 
some  saline  solution,  alcohol  and  ether. 

I.  Crush  about  100  grams  of  ice  (from  the  refrigerator, 
N.  W.  corner  of  laboratory)  by  folding  it  in   a   cloth,  and 
striking  it  with  a  hammer ;  place  it  in  a  beaker,  and  find  the 
reading  of  a  thermometer  when  its  bulb  is  surrounded  with 
the  ice. 

II.  Drain  off  the  water  formed  by  the  melting  of  the  ice, 
and  fill  the  spaces  between  the  fragments  of  ice  with  a  solu- 
tion of  salt  tested  in  Exp.  7  or  8. 

What  is  the  effect  of  salt  in  solution  upon  the  freezing- 
point  of  water? 

III.  Melt  some  paraffine  in  a  porcelain  dish  by  means  of 
an  alcohol  lamp.      Immerse  the  thermometer  bulb  in  the 
melted  paraffine,  remove  it,  and  watch  the  temperature  until 
the  film  of  paraffine  adhering  to  the  bulb  becomes  whitish. 
Then  note  the  temperature. 

Does  the  temperature  fall  uniformly?  or  is  the  fall 
arrested  somewhat  during  solidification?  What  is  the  tem- 
perature of  solidification  of  the  paraffine? 

IV.  Heat  some  water  in  a  beaker.      Hold  the  thermo- 
meter in  the  water,   so  as   not  to   touch  the  sides  of  the 
beaker,  and  note  the  temperature  when  the  film  of  paraffine, 
adhering  to  the  bulb,  becomes  transparent. 

What  is  the  melting-point  of  the  paraffine?  and  is  this 
above  or  below  the  point  of  solidification?  Eepeat  III.  and 
IV.  until  you  feel  sure  of  your  last  answer. 

V.  Heat  some  water  (about  5  cm.  deep)  in  a  test-tube 


20  BOILING  AND   FREEZING-POINTS.  [10 

until  it  boils.       Find  the  reading  of  the  thermometer  in  the 
water,  also  in  the  steam  above  the  water. 

What  is  the  boiling-point  of  this  water  in  this  test-tube? 
and  is  it  higher  or  lower  than  the  point  of  condensation  of 
the  steam?  What  kind  of  thermometer  have  you  employed? 

VI.  Repeat  V.  with  a  ten  per  cent,  solution  of  salt  from 
Exp.  7. 

What  is  the  effect  of  salt  in  solution  on  the  boiling-point 
of  water? 

VII.  Heat  some  water,  5  cm.  deep,  in  a  beaker  to  boiling. 
Remove  it  to  a  safe  distance  from  the  flame.     Fill  a  small 
test-tube  2  or  3  cm.  deep  with  alcohol,  and  immerse  it  in 
the  water  until  it  boils.     If  the  water  is  not  hot  enough, 
heat  it  again,  and  repeat.        Note  the  temperature  at  which 
the  alcohol  boils. 

VIII.  Find  as  in  VII.  the  boiling-point  of  ether,  after 
the  water  has  cooled  to  50°  or  60°.     Take  the  boiling-point 
as  soon  as  possible  after  the  ether  begins  to  boil.        Notice 
whether  the  boiling-point  of  the  ether  is  constant  or  varia- 
ble during  continued  ebullition,  and  explain  this  on  the  as- 
sumption that  the  ether  contains  alcohol,  which  is  less  vola- 
tile than  ether. 


11]  PRESSURE  OF  VAPORS.  21 


11.    PEESSUKE  OF  YAPOKS. 

APPARATUS  :  A  large  and  deep  glass  jar,  containing  a  U- 
tube  closed  at  one  end ;  a  glass  tunnel,  a  thermometer,  and 
a  metre  rod ;  ether,  mercury,  and  access  to  hot  water. 

I.  Fill  a  U-tube,  closed  at  one  end,  with  mercury,  pour- 
ing in  the  mercury,   little  by  little,   from  a  small  beaker, 
through  a  tunnel,  and  working  it  round  the  bend  in  the  tube 
into  the  closed  end,  until  this  and  the  bend  of  the  tube  are 
filled  with  mercury. 

Pour  in  5  or  10  cm.  of  ether,  and  tip  the  tube  so  as  to  let 
about  5  cm.  of  ether  flow  round  the  bend.  "Work  out  all 
bubbles  of  air.  The  column  of  mercury  should  now  stand 
somewhat  lower  in  the  open  branch  than  in  the  closed 
branch  of  the  U-tube.  The  whole  column  of  mercury 
should  be  however  at  least  50  cm.  long,  including  the  bend. 

Now  fill  a  deep  glass  jar  with  water  at  about  55°  Centi- 
grade, from  the  heater  over  the  sink ;  stir  it  thoroughly,  and 
when  it  has  cooled  to  50  ° ,  place  the  U-tube,  containing 
the  mercury  and  the  emprisoned  ether,  in  the  jar. 

Describe  the  phenomena  which  take  place. 

II.  Hold  a   thermometer  in    the   jar  between   the   two 
branches   of  the   U-tube,  and   on   a  level  with   the  small 
column  of  emprisoned  ether.     Note  the  reading  of  this  ther- 
mometer; also,  at  as  nearly  as  possible  the  same  time,  the 
difference  in  level  between  the  two  ends  of  the   mercury 
column  in  the  two  branches  of  the  U-tube. 

As  the  water  cools,  continue  to  take  simultaneous  obser- 
vations of  temperature  and  pressure  as  long  as  may  be 
practicable. 

III.  Calculate  the  pressure  of  the  ether  vapor  in  each 
case  (in  cm.  of  mercury),  remembering  that  the  barometric 
pressure  is  about  76  cm.  of  mercury. 


22  PRESSURE  OF  VAPORS.  [11 

IV.  Plot  a  curve  on  coordinate-paper  representing  the 
pressure  of  ether  vapor  at  different  temperatures,  using  the 
temperatures  observed  in  II.  as  abscissas,  and  the  corres- 
ponding pressures  as  ordinates. 

Find  the  temperature  corresponding  to  a  pressure  of  76 
cm.,  and  compare  it  with  the  boiling-point  of  the  ether  ob- 
served in  Exp.  10.  Why  should  these  results  agree? 

Find  the  pressure  corresponding  to  the  boiling-point  of 
the  ether,  and  compare  this  with  the  barometric  pressure. 
Why  should  these  two  results  agree? 

V.  Kepeat  I. -IV.,  if  time  permits,  with  alcohol,  or  other 
liquid,  after  consultation  with  your  instructor. 


12]  HYGROMETRY.  23 


12.     HYGEOMETEY. 

APPARATUS:  An  air-pump,  a  graduated  bottle,  a  battery 
jar,  a  rubber  tube,  a  drying-tube,  trip  scales,  weights  (1  k. 
to  1  dg.);  a  polished  metal  cup,  a  thermometer,  ice  (or 
nitrate  of  ammonia)  and  a  pair  of  wet-and-dry-bulb  thermo- 
meters. Access  to  sink  and  to  air-pump. 

I.  (1)     To  be  performed  at  the  sink. — Fill  a  graduated 
bottle  with  water,  invert  in  a  battery  jar  full  of  water,  push 
a  rubber  tube  down  into  the  jar  and  up  5  or  10  cm.  into  the 
mouth  of  the  bottle,  and  empty  most  of  the  water  out  of  the 
jar.     Eepeat  until  hardly  any  air  is  found  in  the  bottle. 

(2)  At  the  air-pump.  —  Pull  out  the  piston  of  the  air- 
pump  to  its  fullest  extent ;  connect  the  vent  with  the  rubber 
tube  in  (1),  and  force  as  much  air  as  can  be  measured  into 
the  graduated  bottle. 

Fill  the  bottle  again,  if  necessary,  as  in  (1),  and  measure 
the  air  remaining  in  the  barrel  of  the  air-pump  as  above. 

Express  the  contents  of  Jthe  barrel  in  cu.  cm. 

II.  Carefully  counterpoise  a  drying  tube  (consisting  of  a 
U-tube  filled  with  glass  beads  wet  with  sulphuric  acid)  on 
the  trip  scales.        Lay  it  flat  with  its  centre  of  gravity  over 
the  middle  of  the  scale-pan,  taking  care  not  to  let  any  of  the 
acid  flow  out. 

Force  100  barrel-fuls  of  air  from  the  air-pump  through 
the  tube,  and  find  the  gain  of  weight  due  to  absorption  of 
aqueous  vapor  from  the  air. 

Calculate  the  weight  of  "water  in  1  cu.  cm.  of  air. 

III.  Cool  some  water  in  a  polished  metal  cup,  by  stir- 
ing  in  ice,  little  by  little,  until  a  film  of  moisture   appears 
on  the  outside.      Be  careful  not  to  breathe  on  the  cup.       If 
you  feel  doubtful  about  the  existence  of  a  film,  see  if  you 


24  HYGBOMETEY.  [12 

can  wipe  it  off  in  places  with  your  handkerchief.      Note  the 
temperature  at  which  a  film  appears. 

IV.  Add  water  from  the  faucet,   little  by  little,  until  the 
film   disappears.       Note   the   temperature    at    which    this 
occurs. 

V.  Repeat  III.  and  IV.    alternately  until   the   tempera- 
tures of  appearance  and   disappearance   of  the   film   agree 
within  one  or  two  degrees.     Find  the   mean   of  these   two 
temperatures,  and  note  that  it  is  called  the  "dew-point"  of 
the  air. 

VI.  Note  the  reading  of  the  dry-bulb  and  wet-bulb  ther- 
mometers. 

Which  stands  the  lower?  And  why?  Find  the  differ- 
ence of  the  two  thermometers,  multiply  it  by  1.8,  and  sub- 
tract the  product  from  the  reading  of  the  dry-bulb  ther- 
mometer. How  does  the  result  compare  with  the  dew-point 
determined  in  V? 

NOTE.  While  one  pair  of  students  is  performing  I. -II., 
another  pair  may  perform  III. -VI.,  and  the  reverse. 


13]  PNEUMATICS.  25 


13.    PNEUMATICS. 

APPARATUS  :  *An  air- thermometer,  of  special  construction, 
a  mercurial  thermometer,  a  jar  for  water,  a  beaker,  and  a 
rubber  siphon. 

I.  Place  both  sliders  with  their  upper  edges  opposite 
the  zeros  of  their  mm.  scales,  then  slide   the  glass  gauges 
within  their  clamps  until  the  mercury  stands  at  the  same 
level,  0  mm.,  in  both  gauges. 

Bead  the  space  in  cu.  cm.  occupied  by  the  confined  air  in 
the  closed  gauge.  (The  gauge  is  graduated  to  cu.  cm.  and 
tenths). 

II.  Now  raise  the  open  gauge  until  it  stands  at  about  76 
cm.,  readjust  the  closed  gauge  to  zero  as  in  I.,  then  readjust 
the   open  gauge,  etc.,  etc.;  until,  while   the   closed  gauge 
stands  at  zero,  the  open  gauge  stands  at  76  cm. 

Again  read  the  volume  of  the  air  confined  in  the  closed 
gauge.  What  proportion  does  the  pressure  of  the  confined 
air  in  II.  bear  to  that  in  I.?  What  proportion  does  the 
volume  of  the  confined  air  in  I.  bear  to  that  in  II.? 

III.  Repeat  II.  with   modifications   necessary  to  bring 
the  mercury  in  the  open  gauge  at  zero  and  that  in  the  closed 
gauge  at  25.33  cm. 

What  proportion  does  the  pressure  of  the  confined  air  in 
III.  bear  to  that  in  I.?  What  proportion  does  its  volume  in 
I.  bear  to  that  in  III? 

State  whether  the  law  of  "Boyle  and  Mariotte"  con- 
necting the  pressure  and  volume  of  a  gas  at  a  constant  tem- 
perature, is  or  is  not  illustrated  by  your  experiments,  within 
the  limits  of  errors  of  observation. 

*If  the  old  form  of  apparatus  with  mirror-scale  is  used,  slight  modifications 
of  the  directions  below  will  be  necessary,  and  the  student  should  ask  for  special 
instruction. 


26  PNEUMATICS.  [13 

IV.  Eeplace  the  apparatus  as  in  I.,  only  measure  accu- 
rately the  temperature  of  the  water  surrounding  the  closed 
gauge.     Siphon  off  this  water,  and   replace  with  water  at 
about  60°  Centigrade.  Eeadjust  as  in  I.,  and  again  measure 
the  volume  (in  cu.  cm.)  of  the  confined  air,  and  at  the  same 
time,  observe  the  temperature. 

Calculate  (a)  the  proportion  which  the  new  volume  bears 
to  that  in  I.,  and  (b)  the  proportion  in  which  it  increases  for 
a  rise  of  one  degree  of  temperature.  The  latter  (b)  is  found 
by  subtracting  unity  from  the  result  in  (a),  and  dividing  the 
remainder  by  the  rise  of  temperature  in  question. 

V.  Kaise  the  open  gauge  until  the  confined  air  in  the 
closed  gauge  is  compressed  to  its  orginal  volume,  in  I.  Note 
the  temperature  of  the  water,  and  the  difference  of  level  be- 
tween the  mercury  levels  in  the  two  gauges. 

What  proportion  does  the  pressure  of  the  confined  air  in 
V.  bear  to  that  in  I.?  And  in  what  proportion  does  the 
pressure  of  a  gas  increase,  when  confined  to  a  constant 
volume,  for  one  degree  rise  of  temperature  ? 


14]  EXPANSION  OF  LIQUIDS — BALANCING  COLUMNS.  27 


14.    EXPANSION  OF  LIQUIDS— BALANCING 
COLUMNS. 

APPAEATUS  :  An  expansion  apparatus  similar  to  Gay- 
Lussac's,  a  long  stirrer,  a  rubber  tube ;  a  metre  rod,  and  a 
thermometer. 

I.  Fill  the  inner  system  of  tubes  with  water  from  the 
faucet,  through   a  rubber  tube.      When  a  stream  of   water 
issues  continuously  from  the  open  end,  the  tubes  are  prob- 
ably full.     Make  sure,  however,  that  no  air  is  caught  in  the 
bends   of  the  tubes.       Eock  the  whole  apparatus  several 
times  from  right  to  left,  so  as   to  free  the  bubbles,  if  any. 

Fill  one  of  the  water-jackets  with  cold  water,  the  other 
with  water  as  hot  as  possible.  Draw  this  from  the  heater 
near  the  sink,  in  a  stream  so  slow  that  it  issues  mixed  with 
steam. 

Does  the  water  stand  at  the  same  height  in  the  two 
gauges  ?  How  do  you  explain  this  fact  ? 

II.  Stir  the  hot  water  thoroughly  with  the  long  stirrer, 
and  observe  its  temperature.         At  the  same  time,  measure 
the  difference  of  level  between  the  two  glass  gauges.       Note 
the  temperature  of  the  water  in  the  cold  jacket. 

III.  Pour  out  a  little  of  the  hot  water,  and  replace  with 
cold  water ;  mix  thoroughly,  and  proceed  as  in  II. 

IV.  Make  as  in  II.  and  III.  a  series  of  simultaneous  ob- 
servations of  the  difference  between  the  heights  of  the  two 
hydrostatic  columns,  and  the  corresponding  temperatures. 

V.  Plot  the   results  obtained  in  II.  III.  &  IV.  on   co- 
ordinate paper,  laying  off    the  temperatures  horizontally, 
one  tenth  of   an  inch  to  the  degree,  and  the  differences  of 
level  vertically,  one  tenth  of  an  inch  to  a  millimetre. 

Is  the  expansion  of  water  uniform  or  irregular? 


28  EXPANSION  OP  LIQUIDS — BALANCING  COLUMNS.  [14 

VI.  Find  from  your  curve  the  difference  between  the 
two  columns  of  cold  water  in  the  gauge  at  50°.  Measure 
the  length  of  the  hot  water  column  from  centre  to  centre  of 
the  horizontal  bends,  and  find  the  length  of  the  cold  water 
column  which  balances  it  at  50°,  by  subtracting  the  differ- 
ence between  the  two  columns  of  cold  water  in  the  gauges 
from  the  hot  water  column.  (Ask  why,  if  you  do  not  under- 
stand this).  Calculate  the  relative  density  of  water  at  the 
temperature  of  the  room  and  at  50°. 

Draw  a  tangent  to  the  curve  at  a  point  between  50°  and 
51°;  measure  the  rise  of  this  tangent  in  cm.  of  the  scale  cor- 
responding to  a  rise  of  10°  in  temperature.  Calculate  the 
expansion  in  cm.  of  a  column  of  water  1  cm.  long,  between 
50°  and  51°.  What  is  this  quantity  called?  (Ask  if  you  do 
know). 


15]         EXPANSION  OF  LIQUIDS — SPECIFIC  GRAVITY  BOTTLE.         29 


15.  EXPANSION  OF  LIQUIDS— SPECIFIC  GRAVITY 

BOTTLE. 

APPARATUS.  A  glass  -  stoppered  bottle,  a  thermometer, 
scales  with  weights  to  1  gram,  a  vessel  for  hot  water,  some 
coal-oil,  some  alcohol,  and  a  cloth. 

I.  Find,  as  in  Exp.  4,  the  weight  of  coal-oil  required  to 
fill  a  glass-stoppered  bottle.     Note  the  temperature  of  this 
coal-oil. 

II.  Surround  the  bottle  up  to  its  neck  with  hot  water,  at 
about  30  degrees.     Take  a  cloth,  and  with  it  wipe  off  the 
coal-oil  which  is  forced  out  of  the  bottle,  from  time  to  time 
until  no  more  is  forced  out.     Then  take  the  temperature  of 
the  water,  after  thoroughly  stirring  it.      Take  the  bottle 
out  of  the  water,  wipe  it  dry,  and  find  as  before  the  weight 
of  coal-oil   which  it  contains.      Why  does  the  bottle  hold 
less  coal-oil  than  before  ? 

III.  Repeat  II.  with  water  at  40  ° ,  then  with  water  at 
50  °  ,  60  °  ,  etc.,  up  to  100  °  if  possible.     Note  in  each  case 
the  temperature  and  the  weight  of  the  coal-oil,  determined 
as  before. 

IV.  Plot  the  results  of  II.  and  III.  on  coordinate  paper ; 
draw  a  curve  representing  the  weights  of  coal-oil  filling  the 
bottle  at  different  temperatures ;  prolong  this  curve  by  the 
eye    until     it  reaches   the   zero  of   the   scale   of  degrees, 
and  infer  the  weight    of  coal-oil  which  would  fill  the  bot- 
tle at  0  ° . 

Prolong  the  curve  also  until  it  intersects  the  line  repre- 
senting 100  ° ,  and  infer  the  weight  of  coal-oil  at  100  ° , 
which  would  fill  the  bottle. 

V.  Calculate  the  relative  volume  of  a  given  mass  of  coal- 
oil  at  100  °  referred  to  its  volume  at  0  ° .     Express  this  as 


30  EXPANSION  OF  LIQUIDS— SPECIFIC  GRAVITY  BOTTLE.        [15 

a  ratio,  consisting  of  unity  followed  by  three  places  of 
decimals,  thus  :  l.xxx. 

Find  the  expansion  of  1  cu.  cm.  between  0  °  and  100  ° , 
by  substracting  1.  from  the  relative  volume  above.  This 
will  give  you  a  cipher  followed  by  three  places  of  decimals, 
thus :  O.xxx. 

Calculate  the  expansion  of  1  cu.  cm.  for  one  degree.  Why 
should  this  contain  five  places  of  decimals  ?  What  name  is 
given  to  this  quantity  ?  (Ask  if  you  do  not  know). 

VI.  Repeat  I.-V.  if  time  permits,  with  alcohol  instead 
of  coal-oil. 


16]  LINEAR  EXPANSION.  31 


16.      LINEAE  EXPANSION. 

APPARATUS  :  An  expansion  apparatus,  with  metallic  rod, 
a  metre  rod,  a  thermometer,  a  rubber  tube  for  siphon,  ves- 
sels for  hot  and  cold  water. 

I.  Find   the  length  of  a  metallic  rod,  whose  expansion 
is  to  be  determined,  by  measuring  it  with  a  metre  rod  divi- 
ded into  mm. 

II.  Place  the  rod  in  the  horizontal  trough,  cover  it  with 
water,  take   the  temperature  of    the  water,  and  set  the  mi- 
crometer upon  the  rod. 

A  setting  of  the  micrometer  is  made  as  follows  :  Take 
hold  of  the  screw  by  the  friction  head,  which  slips  when 
the  requisite  pressure  is  attained ;  turn  it  to  the  right  until 
it  slips,  and  see  how  many  whole  mm.  divisions  on  the 
shaft  of  the  screw  are  uncovered.  Head  the  hundredth^ 
of  a  mm.  by  the  indication  of  a  line  parallel  to  the  shaft 
of  the  screw  with  respect  to  the  divisions  on  the  barrel. 
Kepeat  until  concordant  readings  are  obtained,  and  record 
the  mean  of  a  considerable  number  of  such  readings.  In 
a  rod  1000  mm.  long,  the  readings  should  agree  within  a 
few  hundredths  of  a  mm. 

AFTER  EACH  SETTING,  WITHDRAW  THE  POINT  OF  THE 
MICROMETER  AT  LEAST  3  mm.,  so  that  it  may  not  be  injured 
by  expansion  of  the  rod. 

III.  Siphon  off    some  of   the   water,   and  replace  with 
hot  water,     so    as  to    raise   the     temperature    10    or    20 
degrees.*      Note    the   temperature     of     the    water     after 
thoroughly  stirring  it,   and   make  a  new  setting  of  the  mi- 
crometer. 

IY.     Make   simultaneous  observations   of     temperature 

*  The  water  may  also  be  heated  by  Bunsen  burners  placed  beneath  the 
trough. 


32  LINEAR  EXPANSION.  [16 

.and  the  micrometer  at  intervals  of  10  or  20  degrees  as  in 
III,  up  to  at  least  90  ° . 

V.  Siphon  off  some  of   the  hot  water,  and  replace  with 
cold.      Make  in   this   way  a  second   series   of  observations 
of  temperature  and  length  10  or  20  degrees  apart,  down  to 
the  temperature  of  the  room. 

VI.  Cool  the   water  with  a  little  ice,  and  note  the  tem- 
perature and  micrometer  reading  as  before. 

VII.  Plot  all  the  temperatures  and  corresponding  read- 
ings  of    the   micrometer  on   coordinate  paper,    and    draw 
curves  illustrating  the   expansion  and   contraction   of   the 
rod. 

VIII.  Calculate  the  average  expansion,   in  cm.,  of   one 
<cm.  of   the  rod  when  heated  one  degree.      What  name   is 
given  to  this  last  result?       (Ask  if  you  do  not  know.) 


17]          CHANGE  OF  VOLUME  IN  MELTING.  33 


17.   CHANGE  OF  VOLUME  IN  MELTING. 

APPARATUS  :  A  specific  gravity  bottle,  two  battery-jars, 
scales  and  weights  to  one  gram,  a  thermometer,  and  some 
ice. 

I.  Mis  about  300  grams  of  crushed  ice  and  about  300 
grams  of  water  in  a  battery  jar,  and  stir  till  the  tempera- 
ture falls  below  1  °  Centigrade. 

Counterpoise  a  specific  gravity  bottle,  cool  it  in  the  mix- 
ture of  water  and  ice,  and  fill  it  with  cold  water  decanted 
out  of  the  mixture. 

Remove  floating  particles  of  ice,  if  any,  and  insert  the 
solid  glass  stopper  so  as  not  to  include  any  air.  (See 
Exp.  4) 

Dry  the  outside  of  the  bottle,  and  find  the  weight  of  cold 
water  which  it  contains. 

II.  Empty  the  cold  water  back  into  the  jar,  and  fill  the 
bottle  with  pieces  of    ice   as  full  as  may  be  convenient. 
Insert  the  stopper  loosely,  invert  the  bottle,    and    let  as 
much  water  as  possible  drain  off  from  the  ice. 

Find  the  weight  of  ice  contained  in  the  bottle,  making 
the  weighing  as  rapidly  as  possible.  If  much  of  the  ice 
has  melted,  drain  off  the  water  again,  and  reweigh. 

III.  Fill  the  space  in  the  bottle  (not  occupied  by  ice) 
with  water  from  the  jar  at  about  0  ° ,   and  reweigh  the  bot- 
tle. 

Calculate  as  in  Exp.  4,  the  specific  gravity  of  the  ice 
referred  to  water  at  about  0  °  . 

IV.  Place  the  bottle  with  its  contents  in  a  jar  of  water 
at  about  30  ° .      Warm  it  in  this  way  until  all  the  ice  is 
melted,   and  until  the   mixture,   after  being  well  shaken, 
shows  a  temperature   of  8  ° .      Weigh  the  bottle   and  its 
contents. 


34  CHANGE  OF  VOLUME  IN  MELTING.  [17 

Has  any  change  of  volume  taken  place  ?  and  if  so,  what 
kind  of  a  change  ? 

V.  Fill  the  bottle  with  cold  water  at  8  ° ,  and  reweigh 
it. 

How  does  the  density  of  water  at  8  °  compare  with  that 
atO°? 

Find  the  contraction  of  the  ice  in  cu.  cm.,  allowing  1.000 
cu.  cm.  to  the  gram  of  water  at  8  ° . 

Calculate  the  contraction  of  one  gram  of  ice  in  melt- 
ing. 


18]  LATENT  HEAT.  35 


18.    LATENT  HEAT. 

APPARATUS  :  A  Bunsen  burner,  with  cone ;  a  filter  stand, 
with  ring  and  netting ;  a  pint  cup,  a  thermometer,  a  clock, 
and  some  ice. 

NOTE.  THE  HEIGHT  OF  THE  FLAME  MUST  NOT  BE  DIS- 
TURBED THROUGHOUT  THE  EXPERIMENT. 

I.  Nearly  fill  a  pint  cup  with  crushed  ice  ;  drain  off  as 
much  water  as  possible,  and  note  the  temperature. 

Put  an  iron  cone  on  a  Bunsen  burner,  to  steady  the 
flame ;  light  the  flame  and  turn  it  down  until  its  extreme 
length  is  about  10  cm.  Set  it  beneath  a  netting  1  or  2  cm. 
above  the  top  of  the  cone.  Heat  the  ice  for  just  one  min- 
ute. Remove  the  cup,  and  again  note  the  temperature. 
Stir  the  ice  with  your  pencil,  not  with  the  glass  thermom- 
eter. Note  the  temperature  after  stirring. 

Is  stirring  necessary  to  secure  uniformity  of  temperature 
in  a  mixture  ?  Has  the  minute's  heating  raised  or  lowered 
the  temperature  of  the  ice  ?  How  do  you  account  for  this 
fact? 

What  change  of  state  has  taken  place  in  part  of  the  ice  ? 

II.  Heat  the  ice  for  another  minute,  and  proceed  as  in  I. 
What  farther  change  has  taken  place  ? 

III.  Proceed  as  in  II.  to  heat  the  ice  one  minute   at  a 
time  until  after  thorough  stirring  a  distinct  rise  of  temper- 
ature is  observed.     Note  the  temperature  of  the  mixture. 

What  proportion  of  ice  now  remains  in  the  cup  ? 

IV.  Place  the   cup  with  its  contents  over  the  burner  as 
before,  and  note  the  temperature  at  intervals  of  one   min- 
ute until  the  water  boils,  stirring  between  observations,  but 
not  removing  the  cup. 

How  does  the  time  required  to  melt  the  ice  compare  with 


36  LATENT  HEAT.  [18 

the  time  required  to  raise  the  water,  formed  by  its  lique- 
faction, from  0  °  to  100  °  Centigrade  ? 

If  the  rate  of  heating  is  uniform,  how  does  the  heat  re- 
quired to  melt  a  given  weight  of  ice  compare  with  that 
required  to  raise  the  same  weight  of  water  from  the  freez- 
ing to  the  boiling  temperature  ? 

Calling  the  amount  of  heat  necessary  to  raise  a  gram  of 
water  one  hundred  degrees  one  hundred  units,  about  how 
many  units  of  heat  are  necessary  to  melt  one  gram  of 
ice? 

V.  See  how  long  it  takes  to  boil  all  the  water  away 
with  the  same  flame.      Note  the  temperature  from  time  to 
time.      EXTINGUISH  THE  FLAME  AS  SOON  AS  THE  WATER  DIS- 
APPEARS. 

Calculate,  by  the  same  process  of  reasoning  as  in  IV., 
the  number  of  units  of  heat  necessary  to  convert  one  gram 
of  water  into  steam.  What  name  is  given  to  this  last 
quantity  ?  to  the  corresponding  quantity  in  IV.  ? 

VI.  Plot  all  the  results   in  I.-V.  on  coordinate  paper, 
allowing  0.1  inch,   horizontally,   for  one   minute,   and   0.1 
inch,  vertically,  for  5  degrees. 


19]  SPECIFIC  HEAT — METHOD  OF  FUSION.  37 


19.    SPECIFIC  HEAT— METHOD  OF  FUSION. 

APPAEATUS  :  Three  or  more  balls  of  different  materials, 
weighing  about  100  grams,  each ;  a  Bunsen  burner,  a  filter- 
stand,  with  ring;  vessel  for  heating  water ;  trip-scales  > 
weights  from  1000  to  0.1  grams.  A  block  of  ice.  Cot- 
ton "waste,"  or  cotton  "batting". 

I.  Suspend  several  balls  of  different  materials,   but  of 
about  the  same  weight,  in  a  vessel  of  boiling  water. 

Hollow  out  a  cavity  in  a  cake  of  ice  sufficient  to  contain 
the  largest  ball.  Wipe  the  cavity  dry  with  cotton  fibre,  and 
place  one  of  the  balls  in  the  cavity.  The  transfer  from  the 
boiling  water  to  the  cavity  in  the  ice  should  be  made  as 
rapidly  as  possible,  so  as  to  avoid  considerable  loss  of  heat. 

Weigh  off  some  cotton,  previously  wet  and  wrung  out  as 
dry  as  possible ;  cover  the  ball  with  this  cotton,  so  as  to  cut 
off  air-currents;  wipe  up  all  the  water  formed  by  the  melt- 
ing of  the  ice,  and  find  the  amount  thus  melted  by  reweigh- 
ing  the  cotton. 

Find  the  weight  of  the  ball. 

II.  EEPEAT  I.   with   each  of  the  balls.       Answer  the 
following  questions: 

1.  Does  a  given  weight  of  metal  at  a  given  temperature 
always   melt  a  given   amount  of  ice?   or  does  the  amount 
melted  depend  upon  the  material? 

2.  How  many  units  of  heat  were  given  out  by  each  ball? 
Assume  that  (as  you  might  have  found  in  Exp.  18)  one  gram 
of  ice  requires  about  80  units  of  heat  for  its  liquefaction. 

3.  How  many  units  of  heat  are  given  out  by  each  ball, 
on  the  average,  in  falling  one  degree  in  temperature  ? 

4.  How  many  units  of  heat  are  given  out  by  one  gram  in 
falling  100  degrees  in  the  case  of  each  ball  ? 

5.  How  many  units  of  heat  are  given  out,  in  each  case, 
by  one  gram  in  falling  one  degree? 

6.  Which  of  the  quantities  above  represents  the  thermal 
capacity   of   the  ball?    and  which    represents    its  specific 
heat? 


38  SPECIFIC  HEAT  OF  LIQUIDS.  [20 


20.    SPECIFIC  HEAT  OF  LIQUIDS. 

APPARATUS  :  A  tin  or  other  metallic  cup;  a  Bunsen  burner; 
a  filter  stand;  a  tumbler;  a  thermometer;  a  copper  spiral;  a 
balance,  and  weights.  Liquids  to  be  tested. 

I.  Half  fill  a  pint  cup  with  water,  and  heat  the  water  to 
boiling,  over  a  Bunsen  burner.     Immerse  a  copper  spiral  in 
the  boiling  water. 

Weigh  off  in  a  beaker  enough  water  to  cover  the  copper 
spiral,  and  note  the  temperature  of  the  water. 

Lift  the  copper  spiral  out  of  the  boiling  water,  jerk  off  as 
much  water  as  possible,  and  lower  it  immediately  into  the 
beaker  of  cold  water.  Stir  the  water  with  the  spiral  for 
about  one  minute,  both  up  and  down  and  sideways.  Note 
the  temperature  of  the  water. 

Is  the  water  warmer  or  cooler  than  before?     And  why? 

II.  Eepeat  I.  with  as  nearly  as  possible  the  same  weight 
of  coal-oil  instead  of  cold  water  in  the  beaker. 

Is  the  coal-oil  raised  in  temperature  more  or  less  than  the 
same  weight  of  water?  About  how  many  times  more  or 
less?  Try  to  estimate  about  how  much  coal-oil  would  be 
raised  in  temperature  just  as  much  as  the  water. 

III.  Repeat  II.  with  as  much  coal-oil  as  you  think  will 
show  the  same  rise  of  temperature  as  the  water  in  I. 

Is  the  quantity  of  coal-oil  used  too  great  or  too  small? 
Give  reasons  for  your  answer.  Calculate  by  a  comparison 
of  the  results  in  II.  and  III.,  just  how  much  coal-oil  would 
be  equivalent  in  thermal  capacity  to  the  water. 

Calculate  also  the  quantity  of  water  which  would  be  equi- 
valent to  one  gram  of  coal-oil  in  thermal  capacity.  What 
name  is  given  to  this  quantity? 

Why  does  not  the  heat  absorbed  by  the  beaker  affect  the 
results  above  ? 


20]  SPECIFIC  HEAT  OF  LIQUIDS.  39 

Why  are  these  results  unaffected  by  cooling  of  the  spiral? 
or^by  cooling  of  the  sides  of  the  beaker  in  contact  with  the 
air? 


IV.     Repeat  I. — III.,  or  such  parts  of  I. — III.  as  may  be 

necessary,  in  order  to  find  the  specific  heats  of  alcohol, 
glycerine,  and  as  many  other  liquids  as  time  may  permit. 


40  MECHANICAL  EQUIVALENT  OF  HEAT.  [21 


21.    MECHANICAL  EQUIVALENT  OF  HEAT. 

APPARATUS:  A  metre  rod;  a  pasteboard  tube;  a  thermo- 
meter; two  bottles,  containing  each  one  kilogram  of  shot; 
access  to  the  refrigerator. 

I.  Place  a  kilogram  of  lead  shot  in  a  bottle  and  set  it  to 
cool  in  the  refrigerator.  When  the  shot  has  cooled  about 
3  °  below  the  temperature  of  the  room,  take  the  temperature 
accurately  (within  a  tenth  of  a  degree  if  possible),  and  pour 
it  into  the  long  pasteboard  tube  provided  for  this  experi- 
ment. See  that  the  tube  is  securely  closed. 

Raise  one  end  of  the  tube,  letting  the  other  rest  upon  the 
table,  until  the  tube  stands  vertical.  Do  this  so  rapidly 
that  the  shot  is  held  in  its  place  by  centrifugal  force  until 
it  reaches  its  highest  point.  Then  stop  the  motion  as  sud- 
denly as  possible  by  the  force  of  the  hand  ( not  by  a  blow). 
The  shot  should  fall  the  whole  length  of  the  tube  almost 
like  a  solid  mass. 

Eepeat  this  operation  until  the  shot  has  fallen  through 
the  whole  length  of  the  tube  one  hundred  times.  Insert  a 
thermometer  into  the  mass  of  the  shot,  through  a  small 
opening  made  for  this  purpose,  and  note  the  temperature. 
Why  has  the  temperature  risen  above  that  of  the  room  ? 

Measure  the  average  distance  through  which  the  shot 
falls  in  each  case.  Should  the  metre  rod  just  touch  the  shot 
in  this  measurement?  or  should  it  be  driven  into  the  mass 
of  the  shot?  How  do  you  allow  for  the  thickness  of  the 
stopper  ? 

Calculate  the  total  distance  through  which  the  shot  has 
fallen,  and  the  distance  through  which  it  would  have  to  fall 
to  be  raised  one  degree  in  temperature.  How  great  a 
distance  would  one  gram  of  shot  have  to  fall  to  raise  its 
temperature  by  the  same  amount  (one  degree)?  How  much 


21]  MECHANICAL  EQUIVALENT  OP  HEAT.  41 

work  in  gram-centimetres  would  be  required  to  raise  a  gram 
of  shot  one  degree  in  temperature?  How  much  work  would 
be  required  to  raise  one  gram  of  water  one  degree  in  tem- 
perature, if  the  specific  heat  of  lead  shot  is  0.032?  What 
name  is  given  to  this  last  quantity  ? 

II.  Repeat  I.  while  the  tube  is  still  warm  from  the  first 
experiment.     Is  the  rise  of  temperature  greater  or  less  fiian 
before? 

III.  Eepeat  until  concordant  results  are  obtained.  While 
performing  one  experiment,  cool  the  shot  for  the  next,  so 
that  the  tube  may  not  have  time  to  cool  in  the  mean  time. 
Explain  how  the  thermal  capacity  of  the  tube  is  eliminated 
in  this  way.     As  soon  as  the  rise  of  temperature  of  the  shot 
becomes  approximately  known,  cool  the  shot  for  the  next 
experiment  just  half  of  this  amount.     How  does  the  average 
temperature  now  compare  with  that, of  the   room?     Why- 
is  the  effect  of  cooling  eliminated? 


42  ABSOLUTE    HEAT  CONDUCTIVITY.  [22 


22.    ABSOLUTE  HEAT  CONDUCTIVITY. 

APPARATUS  :  A  conduction  apparatus;  a  small  beaker;  a 
steam  generator  with  Bunsen  burner  and  rubber  connecting 
tube;  two  thermometers;  scales  and  weights  from  1000  g.  to 
0.1  g.;  a  kilo,  of  ice;  access  to  hammer  and  cloth  for  powder- 
ing ice;  access  to  clock. 

I.  Fill,  with  crushed  ice,  that  end  of  the  conduction  ap- 
paratus which  is  provided  with  a  single  drainage  tube,  and 
find  the  weight  of  ice  melted  in  ten  minutes,  then  in  another 
ten  minutes,  then  in  a  third  ten  minutes,  etc.,  etc.,  until  (by 
the  agreement  of  two  successive  results)  the  rate  of  melting 
is  known  to  be  constant. 

Calculate  the  rate  of  melting  in  grams  per  minute,  due  to 
conduction  through  the  sides  of  the  apparatus,  convection 
of  air-currents,  etc. 

II.  Fill  a  steam  generator  two  thirds  full  of  water,  place 
a  Bunsen  flame  beneath  it,  and  raise  the  water  to  boiling. 

Turn  the  spout  so  that  any  overflow  of  water  may  do  as 
litt  le  damage  as  possible.  When  a  jet  of  pure  steam  issues 
from  the  spout,  remove  the  flame  for  a  short  time;  fit  a 
rubber  tube  over  the  spout,  and  connect  the  other  end  of 
the  tube  with  the  conduction  apparatus.  Replace  the 
b  urner  beneath  the  steam  generator. 

Find  as  before  the  weights  of  ice  melted  in  successive 
periods  of  ten  minutes  each,  until  the  rate  of  melting  be- 
comes constant;  and  calculate  the  rate  of  melting  as  before, 
in  grams  per  minute. 

Why  is  the  rate  of  melting  more  rapid  in  II.  than  in  I.? 

III.  Place  two  thermometers  in  the  holes  provided  for 
this  purpose,  while  the  steam  is  still  running  through  the 
apparatus;  and  find  in  this  way  the  difference  of  temperature 
between  two  points  in  the  metallic  rod,  through  which  the 


22]  ABSOLUTE    HEAT  CONDUCTIVITY.  43 

greater  part  of  the  heat  is  conducted  from  the  steam  cham- 
ber to  the  ice  chamber.  Measure  the  distance  between 
these  holes,  and  the  diameter  of  the  rod. 

Calculate  the  cross-section  of  the  rod  in  square  centi- 
metres, and  the  number  of  units  of  heat  which  flow  through 
the  rod  in  1  second,  remembering  that  it  takes  about  80 
units  of  heat  to  melt  one  gram  of  ice,  and  60  sec.  to  make  1 
minute. 

Calculate  the  difference  in  temperature  between  the  two 
points  in  the  rod,  and  the  difference  in  temperature  between 
two  points  one  cm.  apart,  by  simple  proportion. 

Calculate  the  number  of  heat  units  which  would  flow 
through  a  rod  of  the  same  material  one  sq.  cm.  in  cross-sec- 
tion with  a  difference  of  temperature  amounting  to  one  de- 
gree per  cm.,  assuming  that  the  flow  of  heat  is  proportional 
to  the  cross-section  and  to  the  difference  of  temperature 
per  cm. 

What  name  is  given  to  this  latter  quantity?  (Ask  if  you 
do  not  know). 


44  RELATIVE    CONDUCTIVITY  AND  DIFFUSIVITY.  [23 


23.     EELATIVE  CONDUCTIVITY  AND  DIFFUSIVITY. 

APPARATUS  :  A  rod  half  iron,  half  brass,  ruled  in  inches; 
a  similar  rod  constructed  of  two  other  metals;  lead  shot  and 
bees'  wax;  a  Bunsen  burner;  an  Ingenhousz'  apparatus;  a 
thermometer;  access  to  hot  water,  and  to  a  clock. 

I.  Fill  the  Ingenhousz'   apparatus  with   water  at  60  ° . 
When  the  wax  on  the  several  rods  has  melted  as  far  as  it 
will  melt, — say  after   5,  10,  or   15   minutes, — note   the  dis- 
tance through  which  it  has  melted  on  each  rod.       This  can 
be  determined  BY  THE  TOUCH  within  a   centimetre  or  less. 

Arrange  the  different  materials  of  which  the  rods  are 
composed  in  their  order  of  conductivity. 

II.  Kepeat  I.  with  water  at  70  °  ,  at  80  °  ,  etc.     How  do 
the  results  thus  obtained  compare  with  those  in  I.? 

III.  Fasten  a  row  of  lead  balls  one  inch  apart  with  bees' 
wax  to  a  rod  of  iron  and  brass  joined  in  the  middle.       Heat 
the  junction  by  a  Bunsen  burner.     Note  the  time  it  takes  to 
melt  off  each  ball. 

Does  iron  or  brass  diffuse  temperature  the  more  rapidly  ? 
Calculate  the  relative  rates  of  diffusion  of  temperature  from 
the  observed  times  required  to  melt  off  the  first,  second,  and 
third  ball  in  the  case  of  each  metal.  What  name  is  given  to 
that  property  in  solids  which  enables  them  to  diffuse  tem- 
perature rapidly? 

IV.  Eepeat  III.  with  a  rod  similar  to  that  in  III.,  but 
composed  of  two  other  metals. 

V.  Show  that  differences  between  relative  conductivity 
and  relative  diffusivity  may  be  explained  as  the  result  of 
differences  in  specific  heat. 

VI.  Point  out  any  differences  which  may  be  apparent  be- 
tween the  order  of  conductivity  and  the  order  of  diffusivity 
in  different  metals. 


24]  RADIOMETRY.  45 


24.    KADIOMETKY. 

APPARATUS  :  Two  similar  metallic  vessels,  one  polished, 
the  other  blackened;  a  large  beaker;  a  lamp,  a  thermometer, 
and  a  metre  rod;  access  to  clock. 

I.  Hold  your  hand  near  one  side  of  the  lighted  flame, 
then  above  it.  Note  any  difference  in  warmth  that  may  be 
felt. 

Now  put  your  hand  in  the  glass  beaker,  and  repeat  the 
experiment,  taking  care  not  Jo  crack  the  glass  by  bringing 
it  too  near  the  flame.  Can  heat  be  felt  through  the  glass 
instantly,  or  only  after  the  glass  has  had  time  to  become 
warm? 

What  reason  have  you  for  thinking  that  air-currents  are 
concerned  in  carrying  some  of  the  heat  in  certain  directions? 

What  reason  have  you  for  thinking  that  air  currents  are 
not  the  sole  means  of  carrying  heat? 

Why  cannot  the  transference  of  heat  through  the  glass 
be  explained  by  the  ordinary  (slow)  process  of  conduction  ? 

Explain  the  separate  functions  of  conduction,  convection, 
and  radiation  in  this  experiment. 

II.  Fill  the  polished  and  the  blackened  metallic  vessels 
with  boiling  water,  and  note  the  temperature    of  each  for 
several  minutes.       Which  cools  the  more  rapidly  and  why  ? 
(Ask  if  you  do  not  know). 

Give  some  idea  of  the  relative  magnitude  of  the  cooling 
effects  due  to  convection  and  radiation. 

III.  Fill  both  the  polished  and  the  blackened  metallic 
vessels  with  cold  water,  and  set  them  in  the  sun,  or  at  the 
same  distance  from  the  lamp-flame — say  3  inches. 

Which  vessel  is  warmed  the  more  rapidly  and  why? 
Taking  this  single  case  as  an  instance  of  a  general  law,  state 


4:6  KADIOMETRY.  [24 

whether  the  best  radiators  are  the  best  absorbers  of  radiant 
heat,  or  the  reverse. 

IY.  Bring  the  blackened  metallic  vessel  filled  with  cold 
water  as  near  as  practicable  to  the  flame,  and  find,  by  ob- 
servations lasting  a  suitable  length  of  time,  the  average  rate 
of  increase  of  temperature  in  one  minute. 

Then  repeat  the  observations  at  twice  the  distance  from 
the  centre  of  the  flame. 

If  the  radiation  of  heat  is  proportional  to  some  integral 
power  of  the  distance,  directly  or  inversely,  what  is  the 
power  in  question? 


25]  RUMFORD'S  PHOTOMETER.  47 


25.    RUMFORD'S  PHOTOMETER 

APPARATUS:  A  screen  with  rod  to  cast  shadow;  a  group 
of  four  candles ;  a  single  candle  ;  a  coal-oil  lamp ;  a  metre 
rod ;  scales  and  weights  from  1  kilo,  to  1  gram;  access  to  a 
clock. 

I.  Set  the  screen  in  such  a  position  that  the  light  from 
the  windows  casts  no  shadow  of  the  rod  upon  it.     Light  the 
single  candle,  set  it  at  a  distance  of  50  cm.  from  the  screen, 
and  so  as  to  cast  a  shadow  of  the  rod  near  the  middle  of  the 
screen,  but  wholly  on  one  side  of  the  middle  point.       Light 
the  group  of  four  candles,  and  trim  their  wicks  so  that  the 
height  of  the  flames  may  be  as  nearly  as  possible  equal  to 
that  of  the  single  candle.        Eepeat  this  adjustment  from 
time  to  time  throughout  the  experiment. 

Set  the  group  of  four  candles  at  such  a  distance  and  in 
such  a  direction  from  the  screen  as  to  cast  a  shadow  of 
equal  intensity  with,  and  adjacent  to,  that  cast  by  the 
single  candle.  Measure  carefully  the  average  distance  of 
the  group  of  four  candles  from  the  screen.  Repeat  I.  until 
concordant  results  are  obtained. 

How  do  you  know  that  two  lights,  casting  shadows  of 
equal  intensity  upon  a  screen,  produce  upon  this  screen 
equal  degrees  of  illumination  ? 

Assuming  that  the  light  of  four  candles  is  four  times  as 
great  as  that  of  a  single  candle,  and  that  brilliancy  of  illu- 
mination varies  directly  or  inversely  as  some  power  of  the 
distance,  what  is  the  power  in  question?  And  is  the  vari- 
ation direct  or  inverse?  What  is  the  law  connecting  the 
candle-power  of  each  light  with  the  distance  at  which  equal 
brilliancy  of  illumination  is  produced? 

II.  Repeat  I. with  the  group  of  four  candles  at  a  distance 


48  EUMFOBD'S  PHOTOMETER.  [25 

of  50  cm.  from  the  screen,  and  adjusting  the  distance  of  the 
single  candle  until  shadows  of  equal  intensity  are  produced. 

III.  Find  by   appropriate    measurements    the    candle- 
power  of  a  coal-oil  lamp,  by  comparison  with  the  group   of 
four  candles. 

IV.  Find  the  rate  of  consumption  of  the  group  of  candles 
and  of  the  lamp  in  III.  in  grams  per  minute,  by  observing 
in  each  case  the  loss  of  weight  in  a  given  time. 

Calculate  from  III.  and  IV.  the  relative  illuminating 
power  of  the  candles  and  the  lamp  for  equal  weights  con- 
sumed. 


26]  COLOR  PHOTOMETRY.  49 


26.    COLOK  PHOTOMETEY. 

APPARATUS:  A  lamp;  a  white  screen;  colored  papers; 
transparent  red,  green  and  violet  glasses  or  shields;  a  metre 
rod;  a  set  of  Maxwell's  discs,  with  rotating  stand;  and  access 
to  a  dark  room. 

I.  Hold  a  piece  of  red  paper  between  the  lamp  and  the 
white  screen  (in  the  dark  room),  at  such  a  distance  from  the 
lamp  that  the  red  paper  seems  as  brightly  illuminated  as 
the  white  screen  does  (in  parts  not  shaded  by  the  red  paper) 
when  viewed  through  a  piece  of  red  glass. 

Measure  the  distance  of  the  paper  and  that  of  the  white 
screen  from  the  centre  of  the  lamp-flame. 

Calculate  from  these  distances  the  relative  proportion  of 
red  light  reflected  by  the  colored  paper  and  by  the  white 
screen,  making  use  of  the  law  connecting  brilliancy  of  illu- 
mination with  distance,  already  worked  out.  (See  Exp.  25). 

II.  Find  as  in  I.  the  amount  of  green  light  (if  any)  re- 
flected by  the  red  surface,  substituting  for  this  purpose  a 
piece  of  green  glass  instead  of  a  piece  of  red  glass  in  front 
of  the  eye. 

III.  Find  as  in  I.  the  relative  amount  of  violet  light  re- 
flected by  the  red  surface,  making  use  of  a  violet   shield 
(consisting  of  a  solution  of  sulphate  of  copper  in  ammonia). 

IV.  Repeat  I.,  II.  and  III.  with  a  piece  of  green  paper. 

V.  Repeat  I.,  II.  and  III.  with  a  piece  of  ultramarine 
blue  paper. 

VI.  Repeat  I.,  II.   and  III.  with  pieces   of  differently 
colored  papers. 

VII.  Take  a  piece  of  colored  paper  tested  in  VI.,  and 
mount  it  on  a  small  Maxwell's  disc.     Interlock  with  it  black 
and  white  discs  of  the  same  size.      Interlock  three   large 


50  COLOR  PHOTOMETRY.  [26 

discs,  red,  green  and  blue,  to  correspond  with  the  colors 
tested  in  I. — V.,  also  a  black  disc,  and  mount  all  seven  discs 
on  the  rotating  stand,  the  small  discs  in  front  of  the  large 
discs. 

Expose  sectors  of  red,  green,  and  blue  to  correspond  with 
the  proportions  of  red,  green  and  violet  light  already  found 
in  the  paper  tested  in  VI.  See  whether  the  disc  covered 
with  this  paper  matches  the  larger  discs  in  color  when 
rotated  rapidly.  If  not,  make  them  match  as  nearly  as 
possible  (a)  by  throwing  in  more  black  into  the  central  or 
into  the  peripheral  portions;  (b)  by  throwing  more  or  less 
white  into  the  central  portion,  and  (c)  by  changing  the  pro- 
portion of  red,  green  and  blue. 

How  does  the  average  amount  of  red  in  the  outer  parts 
compare  with  that  in  the  inner  circle  ?  How  in  the  same 
way  do  the  amounts  of  green  and  violet  compare? 


27]  FOCI  OF  MIBBOES.  51 


27.    FOCI  OF  MIEKOES. 

APPARATUS:      A  concave  mirror;  two  candles,  a  screen  and 
a  metre  rod. 

I.  Focus  the  window  bars  (looking  west)  on  the  screen, 
by  means  of  the  concave  mirror.        Measure  the  distance 
from  the  mirror  to  the  screen.       Then  focus  the  trees  or 
buildings  in  the  extreme  distance  upon  the  screen.       Again 
measure  the  distance  of  the  mirror  from  the  screen.       Must 
the  distance  between  the  mirror  and  the  screen  be  increased 
or  decreased  to  bring  this  change  about?      Which  of  the 
distances  measured  is  equal  to  the  "  principal  focal  length  " 
of  the  mirror?        Is  it  accurate  enough  to  make  use  of  the 
window-bars  in  finding  the  principal  focal  length   of  the 
mirror? 

II.  Place  the  screen  at  a  distance  from  the  mirror  equal 
to  twice  its  principal  focal  length.      Light  a  candle,  and  set 
it  as  close  to  the  screen  as  can  be  done  without  danger  of 
burning  it.       Turn  the  mirror  until  the  image  of  the  candle 
nearly   coincides  with  the  candle  itself,  and  adjust  the  dis- 
tance of  the  screen  from  the  mirror,  if  necessary,  so  as  to 
give  the  sharpest  possible  definition.     What  is  the   radius 
of  curvature  of  the  mirror?  and  why? 

III.  Light  a  second  candle,  set  it  at  a  measured  distance 
— about  6  inches — from  the  first  candle,  and   as  near  the 
screen  as  may  be  practicable.        How  does  the  distance  be- 
tween the  images  of  the  two  candles  compare  with  that  be- 
tween the  candles  themselves? 

IV.  Place  the  screen  at  a  distance  from  the  mirror  equal 
to  five  times  its  principal  focal  length.      Turn  the  mirror,  if 
necessary,  so  as  to  form  two  spots  of  light  on  the  screen, 
then  move  the  candles  to  or  from  the  mirror  (note  which) 
until  a  clear  focus  is  obtained.       Measure  the  distance  of 


52  FOCI  OF  MIRRORS.  [27 

the  candles  from  the  mirror.  Measure  also  the  distance  be- 
tween the  images  of  the  candles,  and  between  the  candles 
themselves. 

How  does  the  proportion  which  the  distance  between  the 
candles  bears  to  the  distance  between  their  images  compare 
with  the  proportion  which  the  distance  between  the  candles 
and  the  mirror  bears  to  the  distance  between  the  images 
and  the  mirror?  How  (if  at  all)  would  you  modify  the 
statement  in  the  last  question  if  the  distances  of  the  candles 
and  their  images  were  to  be  measured  from  the  centre  of 
curvature  of  the  mirror  (see  II.)  instead  of  from  the  mirror 
itself? 

Find  a  relation  between  the  reciprocals  of  the  distances 
of  the  candles  and  their  images  from  the  mirror,  the  recip- 
rocal of  the  principal  focal  length  of  the  mirror,  and  the 
reciprocal  of  the  radius  of  curvature. 

V.  Repeat  IV.  with  the  positions  of  the  candles  and  the 
screen  interchanged.  Answer  all  the  questions  under  IV. 
anew. 


28]  FOCI  OF  LENSES.  53 


28.    FOCI  OF  LENSES. 

APPARATUS:  A  converging  lens,  a  screen,  two  candles,  a 
metre  rod  and  access  to  a  window  with  a  distant  view. 

I.  Focus  the  window-bars  (looking  west)  on  the  screen 
by  means  of  the  converging  lens,  and  measure  the  distance 
between  the  lens  and  the  screen.     Then  focus  the  trees, 
etc.,  in  the  extreme  distance.     Again  measure  the  distance 
of  the  lens  from  the  screen.     Must  the  lens  and  the  screen 
be  made  to  approach  or  to  recede  in  order  to  bring  this 
change  about?     Which  of  the  measurements  represents  the 
"principal  focal  length"  of  the  lens?     Is  it  accurate  enough 
to  use  window-bars  in  finding  the  principal  focal  length  of 
a  lens? 

II.  Light  two  candles,  place  them  at  a  measured  distance 
— about  six  inches — from  each  other  in  the  middle  of  the 
table,  and  set  the  lens  at  a  measured  distance   from   the 
candles  equal  to  twice  the  principal  focal  length  of  the  lens. 
(See  I.)     Set  the  screen  so  that  the  candles  will  be  focussed 
upon  it.     Measure  the  distance  of  the  lens  from  the  screen, 
also  the  distance  between  the  images  of  the  candles. 

How  do  the  distances  of  the  lens  from  the  screen  and 
from  the  candles  compare  ?  How  does  the  distance  between 
the  images  of  the  candles  compare,  under  these  circum- 
stances, with  the  distance  between  the  candles  themselves? 

III.  Place  the  lens  at  a  measured   distance  from   the 
candles  equal  to  five  times  the  principal  focal  length  of  the 
lens,  and  move  the  screen  so  that  both  candles  are  focussed 
upon  it.     Measure  the  distance  from  the  lens  to  the  screen, 
also  the  distances  between  the  candles  and  between  their 
images. 

Find  a  proportion  between  the  four  distances  in  question. 
Find  also  a  relation  between  the  reciprocals  of  the  distances 


54  FOCI  OF  LENSES.  [28 

of  the  lens  from  the  candles,  and  from  the  screen,  and  the 
reciprocal  of  the  principal  focal  length  of  the  lens. 

IV.  Repeat  III.  with  the  distances  of  the  lens  from  the 
screen  and  from  the  candles  interchanged.      How   is  the 
proportion  in  III.,  and  how  is  the  relation  between  the  re- 
ciprocals in  III.  affected  by  this  interchange  ? 

V.  State  all  points  of  analogy  and  difference  which  may 
become    obvious  on  comparing   this  with  the   preceding 
exercise  (Exps.  27  and  28). 


29]  PHOTOGRAPHIC    CAMERA.  55 


29.    PHOTOGKAPHIC  CAMEKA. 

APPARATUS:  A  photographic  camera,  with  a  tripod;  a 
plate-holder ;  two  plates ;  two  trays  ;  10  g.  ferrous  sulphate  ; 
30  g.  potassic  oxalate ;  15  g.  sodic  hyposulphite ;  3  beakers ; 
a  steel  "diamond;"  access  to  dark  room  with  ruby  light  and 
water. 

I.  TRYING  THE  PLATE-HOLDER.     Practice  this  with  a  dis- 
carded plate,  in  the  light,  until  you  be  come  used  to  the  plate- 
holder.   Be  sure  that  the  slide  fits  perfectly,  so  as  to  leave  no 
crack  through  which  light  may  enter.     Mark  a  line  showing 
how  far  the  slide  must  be  drawn  out  before  the  plate  begins 
to  be  exposed,  and  another  line  to  show  how  far  it  must  be 
drawn  out  to  expose  the  whole  plate.     Divide  this  distance 
into  12  parts.     Practice  cutting  up  a  discarded  plate  into 
strips  with  a  diamond  applied  to  the  glass  (not  film)  side  of 
the  plate. 

II.  PUTTING  A  PLATE  IN  THE  PLATE-HOLDER.      Ask  for  a 
red  light  in  the  dark  room ;  take  a  box  of  plates  in  with 
you,  close  the  door  and  see  that  no  one  opens  it  during  this 
process.     Close  up  chinks,  in  so  far  as  possible,  so  as  to 
exclude  all  white  light  from  the  room.     Open  the  box  of 
plates,  and  remove  the  black  paper  from  one  or  more  of 
them.      Take  out  one  plate,  handling  it  by  the  EDGES,  and 
being  careful  not  to  touch  the  film  side.     Lay  the  plate  in 
the  plate-holder,  film  side  out,  and  close  the  slide.     RETURN 
THE  REST  OF  THE  PLATES,  carefully  wrapped  up,  as  you  found 
them  to  their  box,  and  put  on  the  cover  (or  covers)  of  the 
box.     The  door  may  now  be  opened. 

III.  ADJUSTING  THE  CAMERA.     Set   up  the  tripod   at  a 
distance  from  the  object  you  wish  to  photograph  such  that 
this  object  subtends  the  proper  visual  angle — 30-60  degrees. 
Bring  it  as  nearly  as  possible  on  a  level  with  the  middle 


56  PHOTOGRAPHIC   CAMERA.  [29 

point  of  the  object,  and  level  it  by  adjusting  the  legs. 
Focus  the  object  roughly  on  the  ground  glass,  by  drawing 
out  the  latter.  Raise  or  lower  the  lens,  by  sliding  the  front 
of  the  camera,  until  the  middle  of  the  image  comes  into  the 
middle  of  the  glass.  Do  not  tip  the  camera,  if  you  can  avoid 
it,  to  bring  this  result  about;  and  in  any  case  keep  the 
ground  glass  vertical.  If  the  image  of  the  object  is  too 
small,  bring  the  camera  nearer;  if  too  large,  move  the  camera 
farther  off,  and  readjust  as  before. 

IY.  ACCURATE  FOCUSSING.  In  accurate  focussing,  use  the 
largest  aperture.  If  the  edges  of  portions  of  the  image  are 
colored,  adjust  so  that  they  may  be  red,  rather  than  blue. 
If  you  cannot  focus  exactly,  pull  the  camera  out  a  little  too 
far,  then  push  it  in  a  little  too  far,  so  as  to  produce  equal 
indistinctness  in  both  cases,  then  set  it  half-way  between 
these  limits. 

V.  TESTING  A  PLATE.     Focus  the  camera  as  in  IV.  upon  a 
brick  wall,  in  shadow.     Remove  the  ground  glass,  and  set 
the  plate-holder  in  its  place.     Use  the  smallest  aperture  for 
this  process.     Cap  the  lens,  and  pull  out  the  slide  so  as  to 
expose   about  one  twelfth  of  the  plate.     Remove  the  cap, 
and  expose  the  plate  16  minutes. 

Draw  out  the  slide  so  as  to  expose  another  twelfth  of  the 
plate  8  minutes.  Make  successive  additional  exposures, 
of  successive  additional  twelfths  of  the  plate  as  follows: 
4  min.,  2  min.,  1  min.,  30  sec.,  16  sec.,  8  sec.,  4  sec..  2  sec., 
1  sec.,  and  again  1  sec.  Immediately  cap  the  lens,  and 
close  the  slide.  Take  the  plate-holder  to  the  dark  room. 

VI.  PREPARING  THE  OXALATE  DEVELOPER  AND  FIXING  SOLU- 
TION.    Make  a  solution  of  10  grams  of  ferrous  sulphate  in 
30  grams  of  water. 

Make  another  solution  of  30  grams  of  potassic  oxalate  in 
90  grams  of  water.  (It  is  well  to  add  from  1  to  2  grams 
of  potassic  bromide  to  this  solution). 

Make  a  third  solution  of  15  grams  of  hyposulphite  of 
sodium  in  60  grams  of  water.  This  is  called  the  fixing  so- 
lution. Pour  it  into  a  glass  tray  especially  devoted  to  this 
purpose,  and  make  sure  that  it  is  in  the  dark  room  before 
beginning  to  develop. 


29]  PHOTOGRAPHIC  CAMERA.  57 

VII.  TRYING  THE  DEVELOPER.    Mix  half  of  your  iron  so- 
lution (20  g.)  with  half  of  your  oxalate  solution  (60  g.)  in  a 
developing  tray,  in  the  dark  room,  and  exclude  all  but  red 
light  as  in  II. 

Take  the  plate  out  of  the  plate-holder,  and  cut  it  into- 
five  strips,  lengthwise,  by  means  of  a  diamond.  Immerse 
one  of  the  strips  in  the  developing  solution.  Rock  the 
developer  for  8  minutes. 

Then  immerse  another  strip  with  the  first  for  4 
minutes ;  then  still  another  for  2  minutes  ;  then  another  for 
1  minute,  and  finally  all  five  strips  for  1  minute.  ' 

When  the  last  minute  is  up,  immediately  flood  the  strips 
with  water  from  the  faucet,  and  after  they  have  been 
washed  a  minute,  place  them  in  the  hyposulphite  solution. 

VIII.  FIXING  IMAGES.     Leave  the  strips  in  the  "fixing" 
(hyposulphite)  solution  until  the  edges  become  clear.     The 
door  may  now  be  opened.      Wash  the  strips  15   minutes* 
under  the  faucet. 

IX.  INTERPRETING  RESULTS.     Hold  up  the  strips  to  the 
light.     Sixty  areas  should  now  be  visible,  that  is   12  areas 
on  each  of  the  five  strips,  due  to  different  degrees  of  ex- 
posure.    Which  of  these  areas  shows  the  best  image  of  the 
bricks?    How  long  was  this  area  exposed?    How  long  was 
it  developed?      (Add   all  the   separate   times   concerned). 
What  is  the  best  time  for  exposure?    for    development? 
Note  that  the  method  employed  enables  you  to  find  this  out 
for  yourself  with  any  kind  of  plate,  any  lens,  any  aperture, 
any  illumination,  and  any  developer  by  sacrificing  a  single- 
plate. 

X.  MAKE  A  NEGATIVE  with  the  information  obtained. 


58  PHOTOGRAPHIC    PRINTING.  [30 


30.    PHOTOGRAPHIC  PRINTING. 

APPARATUS  :  A  printing  frame;  a  sheet  of  platinotype 
paper;  two  trays;  developing  or  toning  solution;  fixing  solu- 
tion; also  a  sponge;  some  smooth  (not  porous)  paper,  a 
pestle  and  mortar,  some  citrate  of  iron  and  ammonia,  and 
.some  red  prussiate  of  potash.  Access  to  a  moderately  dark 
room. 

I.  Prepare   some  "blue-print"  paper  as    follows:    to   1 
gram  citrate  of  iron  and  ammonia  add  1  gram  red  prussiate 
of  potash;  pulverize  together  in  a  mortar,  add  10  grams  of 
water  in  the  dark,  and  stir  thoroughly.     Wet  a  small  sponge, 
wring  it  out  dry,  and  dip  it  in  the  mortar  containing  the 
mixture.     Lay  a  sheet  of  waste  paper  on  the  floor,  and  on  it 
a  sheet  of  white  paper  to  be  sensitized.     Run  over  the  whole 
surface   rapidly   with  the   sponge   in  strokes   first  length- 
wise, then  breadthwise  with  respect  to  the  paper.     Hang  the 
paper  up  in  a  dark  place  to  dry  for  at  least  15  minutes,  or 
better  one  hour  before  using.     Meanwhile  proceed  with  the 
following  experiments. 

II.  Put  a  piece  of  "platinotype"  paper  under  the  negative 
obtained  in  Exp.  29,  or  under  some  other  negative;  clamp  it 
in  the  printing  frame,  and  expose  it  to  the  light  of  the  sun 
until  the  paper  begins  to  darken  in  spots  where  the  negative 
does  not  protect  it. 

To  examine  the  print,  take  it  into  the  dark  room,  or  into 
the  shade,  and  lift  up  ONE  SIDE  ONLY  of  the  printing  frame, 
so  that  the  print  will  go  back  into  place. 

About  5  minutes  will  be  required  in  full  sunlight;  about 
20  minutes  in  skylight,  and  about  2  hours  in  a  cloudy  day. 

III.  When  the  print  is  dimly  visible,  remove  it  (in  the 
dark  room)  from  its  frame;  and  cover  it,  in   a  developing 


30]  PHOTOGRAPHIC    PRINTING.  59 

tray,  with  a  nearly  saturated  solution  of  oxalate  of  potash, 
called  the  "developing  solution". 

When  the  print  is  fully  developed  (darkened),  "fix"  it  by 
soaking  it  in  a  solution  of  one  part  hydrochloric  acid  in  100 
parts  of  water,  called  the  "fixing  solution".  Then  wash  it 
in  pure  water,  and  dry  it. 

IV.  Now  make  a  print  on  the  blue-print  paper  which  you 
have  prepared.  This  should  be  exposed  about  4  times  as 
long  as  the  platinotype  paper.  The  print  does  not  need  to 
be  developed,  but  must  be  fixed.  This  is  done  by  soaking 
it  in  pure  water  for  about  5  minutes. 

If  time  remains,  ask  instructions  for  toning  your  blue- 
print, or  for  making  prints  by  other  processes. 


60  DRAWING  SPECTRA.  [31 


31.    DKAWING  SPECTKA. 

APPARATUS  :  A  spectroscope;  Bunsen  burner;  platinum 
wires;  specimens  of  salts,  and  colored  glasses. 

I.  Light  a  Bunsen  flame,  place  it  EXACTLY  in  front  of  the 
slit  of  the  spectroscope,  and  hold  a  wire,  dipped  into  a  salt 
of  sodium,  in  the  lower  part  of  the  flame. 

Turn  the  telescope  (if  necessary)  until  the  yellow  band 
due  to  sodium  appears;  and  focus  the  telescope  upon  this 
band.  Narrow  the  slit  as  much  as  may  be  practicable  with- 
out showing  irregularities  in  the  illumination. 

Bring  the  scale  in  focus  by  its  own  motion,  without  dis- 
turbing the  focus  of  the  telescope  upon  the  slit.  Then  slide 
the  scale  by  the  screw  or  screws  intended  for  this  purpose, 
until  No.  5  (or  50)  of  the  scale  comes  opposite  the  sodium 
band. 

Draw  a  scale  6  inches  long,  representing  the  scale  of  the 
spectroscope,  and  opposite  the  5  (or  50)  of  this  scale  draw  a 
vertical  line,  about  half  an  inch  long,  to  represent  the 
sodium  band.  Note,  in  the  drawing,  the  color  of  the  band; 
also  the  color  of  the  Bunsen  flame.  If  there  are  any  other 
bands,  draw  them  also  and  note  their  colors. 

II.  Draw  as  in  I.  the  spectrum  of  a  Potassium  salt,  of  a 
Calcium   salt,  of  a  Strontium   salt,  of  a  Barium  salt,  of  a 
Lithium  salt,  and  of  Boracic  acid. 

III.  Draw  the  spectrum  of  a  luminous  flame,  also  of  a 
luminous    flame  seen  through  red  glass,  through  yellow 
glass,  through  green  glass,  and  through  blue  glass.     State 
whether  your  pencil  marks  indicate  dark  or  bright  spaces  in 
the  spectrum. 


32]  DIFFRACTION.  61 


32.    DIFFRACTION. 

APPARATUS:  A  telescope  with  a  piece  of  silk  over  the 
object  glass ;  access  to  two  distant  lamps ;  a  metre  rod ;  a 
thread  counter. 

I.  Place  the  lamp-flames  at  the  height  of  the  eye,  turn 
them   so  as  to  be  seen  edgewise  from  a  distance,  and   set 
them  about  11  cm.  apart;    the  line  joining  the  flames  being 
at  right-angles  with  the  line  of  sight. 

Cover  up  one  of  the  lights.  Draw  the  diffraction  effects 
seen  through  a  handkerchief  without  any  telescope  at  a 
distance  of  about  11  metres  from  the  light. 

Does  the  angular  separation  of  the  diffraction  fringes 
depend  upon  the  distance  of  the  handkerchief  from  the  eye  ? 

State  reasons  for,  or  against,  the  supposition  that  the 
effects  are  due  to  light  transmitted  directly  through  meshes 
in  the  handkerchief. 

II.  Repeat  I.   with   a  piece   of  fine    silk.      Count   the 
threads   in  a  half-cm,  of  the  silk,  and  compare   with  the 
handkerchief  in  I.     Compare  also  the  angular   separation 
of  the  diffraction  images  in  I.  and  II. 

Does  a  fine  or  a  coarse  mesh  produce  the  wider  separa- 
tion of  the  side  images? 

III.  Light  both  flames,  carefully  measure  the  distance 
between  them  perpendicular  to  the  line  of  sight,  and  stand 
off  from  the  flames  until  their  direct  images,  as  seen  through 
the    telescope    and    silk    cloth,    are    separated    by   three 
fringes,  the  central  one  nearly   colorless,   formed  by  the 
overlapping  of  the  diffraction  images  of  the  flames. 

Drop  a  plumb-line  from  the  silk  cloth  to  the  floor,  also 
from  a  point  between  the  two  flames  to  the  floor,  and  find 
the  distance  between  these  two  plumb-lines. 

Find  the  ratio   of  the  distance   between  the  candles   to 


62  DIFFRACTION.  [32 

the  distance  between  the  plumb-lines,  and  note  that  this 
is  approximately  equal  to  the  (small)  angle  subtended  by 
the  flames  at  any  point  in  the  handkerchief.  Divide  this 
angle  by  four  to  find  the  angle  subtended  between  sucessive 
fringes  at  the  same  point. 

Multiply  the  distance  between  threads  of  the  silk  cloth 
by  the  sine  of  the  angle  between  successive  fringes  to  find 
the  mean  wave-length  of  the  light  utilized  in  this  experi- 
ment. (The  sine  of  a  small  angle  is  practically  equal  to  the 
angle  itself.) 

IV.  Repeat  III.  at  such  a  distance  from  the  lamps  as  to 
make  the  central  image  reddish  in  the  middle,  and  greenish 
on  either  side.  The  result  should  agree  approximately  with 
the  wave-length  of  red  light. 

Y.  Eepeat  III.  at  such  a  distance  from  the  lamps  as  to 
make  the  central  image  greenish  or  bluish  in  the  middle, 
and  reddish  on  the  edges.  The  result  should  agree  with 
the  wave-length  of  green  or  blue  light. 

VI.  Eepeat  III.,  IV.,  and  V.,  if  time  permits,  at  such  a 
distance  that  the  space  between  the  direct  images  is  divided 
into  2  or  3,  instead  of  4  parts. 


33]  CHLADNl'S   FIGURES,    ETC.  63 


33.    CHLADNl'S  FIGURES,  ETC. 

APPARATUS:  A  square  and  a  round  brass  plate;  a  vice  for 
clamping  the  same  at  the  centre;  a  bow  (with  resin);  some 
lycopodium  and  sand; — a  steel  spring;  a  steel  or  brass  rod; 
and  two  wooden  knife-edges  for  supporting  the  latter. 

I.  Scatter  sand  lightly  over  the  square  plate,  touch  it  at 
the  corners,  and  draw  the  bow  vertically  across  the  middle 
of  one  side,  as  slowly  as  is  consistent  with  the  production 
of  a  musical  note.     Draw  the  figure  formed  by  the  sand. 

II.  Repeat  I.  with  two  points  damped  between  the  bow 
and  the  corners  of  the  plate,  and  with  a   somewhat  more 
rapid  motion  of  the  bow. 

III.  Repeat  I.  damping  the  middle  of  each  side  and  bow- 
ing the  plate  near  one  corner. 

IV.  Repeat  III.  with  a  somewhat  more  rapid  motion  of 
the  bow. 

V.  See  what  other  figures  you  can  produce.     Place  your 
fingers  where  you  want  a  nodal  line  to  reach  the  edge  of 
the  plate,  and  bow  the  plate  where  you  want  to  destroy  a 
nodal  line. 

YI.  Scatter  a  little  lycopodium  over  the  plate.  Does 
the  lycopodium  collect  where  the  sand  collects?  if  not  where 
is  it  gathered  ? 

VII.  Substitute  a  round  plate  for  a  square  plate.     Damp 
it  at  points  90°    apart,  and  bow  between  these   points. 
Draw  the  figure  formed  by  the  sand. 

VIII.  Repeat  VII.  with  points  60  °  apart. 

IX.  Repeat  VII.  with  points  45  °  apart. 

X.  Repeat  VII.  with  points  36  °  apart. 

XL     Repeat  VII.  with  points  30  °  apart,  etc.^etc. 


64  CHLADNl'S  FIGURES,    ETC.  [33 

XII.  See  as  in  V.  what  other  figures  you  can  produce 
with  the  round  plate.  Also,  test  the  behavior  of  lycopodium. 

Can  the  plate  be  made  to  divide  itself  into  an  ODD  number 
of  vibrating  sectors? 


XIII.  Where  must  the  steel  rod  be  supported  in  order 
that  it  may  ring  for  a  long  time  when  struck?        Where  are 
the  "nodes"  in  this  case? 

XIV.  Clamp  the  steel  spring  at  one  end;  force  it  to  vib- 
rate (with  the  fingers)  at  a  rate  much  more  rapid  than  its 
natural  rate  of  vibration.     Note  the  location  of  any  point 
(or  points)  of  minimum  vibration  which  you  may  discover 
in  this  way.     What  are  such  points  called? 

Does  pitch  or  rate  of  vibration  increase  or  diminish, 
throughout  your  experiments,  with  an  increase  in  the  num- 
ber of  nodes  or  nodal  lines? 


34]  NODES  OF  STRINGS  AND  PIPES.  65 


34.    NODES  OF  STEINGS  AND  PIPES. 

APPARATUS:  A  large  fork,  electrically  maintained  in  vi- 
bration; a  thread  and  weight  attached  to  fork;  a  metre  rod; 
a  V-shape  slot  and  support;  a  resonance  tube  with  siphon 
attachment;  a  jar  of  water;  two  tuning-forks  (440  and  570); 
rubber  rings. 

I.  (MELDE'S  experiment).      Set  the  large  fork  in  vibra- 
tion, and   adjust  the   weight  hanging  from  it  by  a  white 
thread  (if  it  is  necessary  to  adjust  it)  so  that  the  thread 
may   be  thrown   in   vibration  attaining  an  amplitude  of  at 
least  one  cm.  in  certain  places. 

Draw  the  string  as  it  now  appears.  What  name  is  given 
to  the  points  of  minimum  vibration? 

Measure  the  distance  of  each  node  from  the  lower  end  of 
the  string. 

II.  Find  the  effect  of  damping  the  string  at  each  of  the 
nodes  by  a  V-shaped  slot.     Is  the  amplitude  of  vibration 
between  the  damper  and  the  fork  increased  or  diminished? 

III.  Find  the  effect  of  damping  a  string  at  any  point  be- 
tween two  nodes. 

IY.  Eun  down  the  string  with  the  damper,  and  note  the 
points  of  maximum  and  minimum  vibration.  How  do  these 
points  compare  with  the  nodes  and  antinodes  ? 

V.  Increase  the  weight  on  the  string  by  10  or  20  per 
cent.     What  is  the  effect  of  a  slight  change  of  tension  on 
the  power  of  a  string  to  respond  to  a  given  rate  of  vibration? 

VI.  Eun  down  the  string  with  the  damper,   as  in  IV., 
when  it  is  loaded  as  in  V.     What  is  the  effect  of  a  slight  in- 
crease of  tension  on  the  lengths  responding  to  a  given  fork? 


VII.     Set  the  resonance  tube  on  the  floor,  and  raise  the 
jar  of  water  connected  with  it.      As  the  water  flows  into  the 

5 


66  NODES   OF  STRINGS  AND  PIPES. 

tube,  hold  a  vibrating  violin  A-fork  over  the  open  mouth  of 
the  tube.  Mark,  by  rubber  rings,  the  water  levels  causing 
the  note  of  the  fork  to  swell  out. 

Confirm  these  results  as  the  water  flows  out  of  the  tube 
into  the  jar,  lowered  for  this  purpose.  Adjust  the  rings  ac- 
curately by  causing  the  water  level  to  pass  by  them  first  in 
one  direction,  then  in  the  other  direction. 

Make  a  diagram  showing  the  spacing  of  the  rings,  with 
actual  measurements. 

Assuming  that  the  points  where  the  vibration  of  a  column 
of  air  can  be  cut  off  without  prejudice  to  its  rate  of  vibra- 
tion correspond  to  nodes,  as  in  the  case  of  strings,  where 
are  the  nodes  in  a  pipe  stopped  at  one  end? 

VIII.  Repeat  VII.,  if  time  permits,  with  a  treble  C-fork, 
instead  of  a  violin  A-fork.       How  do  the  distances  between 
nodes  compare? 

IX.  Find  the  difference,  if  any,  between  the  depths  of 
water  in  a  large  and  in  a  small  hydrometer  jar  responding 
to  a  given  fork,  and  give  the  dimensions  of  each  jar. 


35]  VIBRATION    OF    RODS.  67 


35.    YIBBATION  OF  KODS. 

APPARATUS:  A  vice;  a  clock-spring;  a  set  of  tuning  forks; 
a  rubber  hammer,  and  access  to  a  clock. 

Strike  the  tuning  forks  only  with  the  rubber  hammer,  so  as  to 
avoid  injury. 

I.  Straighten  the  clock-spring,  and  clamp  it  in  the  vice 
so  as  to  stand  out  horizontally.     To  do  this,  the  plane  of 
the   spring   must  be   vertical.     Increase   or   diminish   the 
length  of  the  free  portion  of  the  spring  until,  when  set  in 
vibration,  it  keeps  time  with  the  clock;  making  one  vibra- 
tion from  side  to  side  and  back  again  in  one  second.       Note 
that    this    is    called    a  COMPLETE  VIBRATION  in    acoustics. 
Measure  the  length  of  the  projecting  portion. 

II.  Change  the  length  of  the  free  part  of  the  spring  until 
it  vibrates  four  times  as  fast  as  before.     Again  measure  the 
length  of  the  projecting  portion. 

Assuming  that  the  time  of  vibration  is  proportional  to 
some  power  of  the  length  of  a  spring,  what  is  the  power  in 
question? 

III.  Eepeat  I.  or  II.  with  some  new  length,  chosen  so  as 
to  verify,  or  disprove,  the   conclusion  in  II.      Is  this  con- 
clusion verified  or  not  ? 

IV.  Test  the  vibration  of  the  spring  for  a  series  of  de- 
creasing lengths,  and  describe  what  you  see  or  hear. 

In  what  respect  do  vibrations  which  you  can  see  and 
count  differ  from  those  which  affect  the  ear  ? 

V.  Adjust  the  length  of  the  spring  until  the  note  which 
it  emits  when  set  in  vibration  agrees   in  pitch   with   the 
largest  tuning  fork  in  your  set.       Measure  the  length  of  the 
free  part  of  the  spring. 


68  VIBRATION  OP   BODS.  [35 

Calculate  the  pitch  of  the  spring  in  complete  vibrations 
per  second,  making  use  of  the  law  obtained  in  II. 

(If  you  cannot  tell  when  the  pitch  of  the  spring  is  the 
same  as  that  of  the  fork,  ask  for  help). 

YI.  Find  as  in  Y.  the  pitch  of  each  of  the  forks  in  the 
set. 

VII.  Find  the  effect  of  sounding  two  forks  of  nearly  the 
same  pitch  at  the  same  time.       Express  this  quantitatively, 
if  possible. 

VIII.  Find  the  effect  of  loading  each  of  the  forks  in  VIL 
with  a  small  quantity  of  wax. 


36]  LISSAJOUS'  CUBYES.  69 


36.    LISSAJOUS'  CUEVES. 

APPARATUS:  A  Blackburn's  pendulum,  a  set  of  rectangular 
rods  forming  Lissajous'  curves;  access  to  a  clock. 

I.  Adjust  the  Blackburn's  pendulum  in  the  shape  of  a  T; 
fill  the  tracer  with  sand;  draw  it  out  diagonally,  then  release 
it,  and  let  it  trace  a  complete  cycle  of  curves  on  a  piece  of 
paper. 

Draw  some  of  the  more  characteristic  curves  traced  by 
the  pendulum. 

Find  the  rate  of  vibration  of  the  pendulum  in  a  direction 
parallel  to  the  plane  of  the  T,  and  also  in  a  direction  at 
right  angles  with  this  plane.  How  do  these  rates  compare? 

II.  Adjust  the  Blackburn's  pendulum  in  the  shape  of  a 
Y,  with  the  stem  of  the  Y  one  fourth  of  the  maximum  radi- 
us of  vibration.     In  other  respects,  repeat  I. 

Why  are  the  rates  of  vibration  in  perpendicular  planes 
now  very  unequal? 

III.  Obtain  as  in  I.  and  II.  drawings  of  curves   repre- 
senting a  variety  of  simple  integral  ratios  between  the  two 
rates  of  vibration  of  the  pendulum.       (  The  most  important 
ratios  are  1:1,  2:1,  3:1,  3:2,  4:3,  etc.) 

IY.  Pull  each  of  the  rods  diagonally,  and  draw  the  vari- 
ous curves  to  which  they  give  rise,  in  so  far  as  it  is  possible 
to  recognize  these  curves. 

In  connection  with  the  drawings  of  the  curves,  note 
whether  the  figures  are  persistent  in  form,  or  whether  they 
pass  through  a  series  of  forms.  In  the  latter  case,  give 
some  idea  of  the  succession  of  forms,  and  whether  this  suc- 
cession is  slow  or  rapid. 

Point  out  every  possible  case  of  resemblance  between  the 
curves  made  by  the  rods  and  those  drawn  by  the  pendulum. 

Assuming  that  the  curves  formed  by  the  rods  are  due, 
like  those  drawn  by  the  pendulum,  to  the  composition  of 
two  vibrations  at  right-angles,  what  do  you  infer  to  be  the 
ratio  between  the  two  rates  of  vibration  irLfiach  case  which 
you  have  recognized? 

"OF  THE 


70  LAWS   OF  STRINGS  AND  PIPES.  [37 


37.    LAWS  OF  STKINGS  AND  PIPES. 

APPARATUS:  A  sonometer  with  pulley  (or  other  means  of 
stretching  a  wire);  2  wires  4  ft.  long,  of  different  weights;  a 
sliding  bridge;  a  metre  scale;  weights  from  1  to  4  kilograms; 
a  set  of  organ-pipes  (or  other  means  of  producing  the  musi- 
cal scale);  also  trip  scales  and  weights. 

I.  Stretch  the    lighter   wire   with   the   lightest    weight 
—  about  1  kilo. — and  move  the  bridge  until  the  note  emitted 
by  the  wire  when  plucked  is  in  unison  with  "  Ut  3  "  of  the 
organ-pipe.      Measure  the  length  of  the  string  under  vibra- 
tion, also  the  depth  of  the  pipe. 

II.  Eepeat  I.  with  about  4  times  the  weight  stretching 
the  string.     If  the  length  of  the  string  is  proportional,  di- 
rectly or  inversely,  to  some  power  of  the  weight  stretching 
it,  what  is  the  power  in  question? 

III.  Eepeat  II.  with  a  series  of  organ-pipe  notes  cover- 
ing an  octave.     What  relation  exists  between  the  lengths  of 
the  string  and  the  depths  of  the  pipe. 

Assume  that  the  rates  of  vibration  of  the  different 
notes  are  proportional  to  the  following  numbers: 
Ut,  24;  Ke,  27;  Mi,  30;  Fa,  32;  Sol,  36;  La,  40;  Si,  45;  Ut,  48: 
find  the  product  of  each  of  these  numbers  by  the  corre- 
sponding length  of  the  string.  State  the  law  connecting  the 
length  of  a  string  with  its  rate  of  vibration. 

Find  in  the  same  way  the  law  connecting  the  length  of 
an  organ-pipe  with  its  rate  of  vibration. 

IV.  Weigh  the  string  used  in  II.,  also  weigh  the  other 
string.     Eepeat  II.  with  the  heavier  string. 

If  the  length  of  a  string  emitting  a  given  note  is  directly 
or  inversely  proportional  to  some  power  of  the  weight  of 
the  string,  what  is  the  power  in  question? 

Summarize  your  results  as  follows: — The  rate  of  vibration 
of  a  string  is  proportional  directly  or  inversely  to  the  xth 
power  (or  root)  of  its  length,  directly  or  inversely  to  the  yth 
power  (or  root)  of  its  tension,  and  directly  or  inversely  to 
the  2th  power  (or  root)  of  its  weight  per  unit  of  length. 


38]  GRAPHICAL  MEASUREMENT  OF  PITCH.  71 


38.    GRAPHICAL  MEASUEEMENT  OF  PITCH. 

APPARATUS:  A  tracing  apparatus;  a  rubber  hammer;  a 
glass  slide;  powder,  and  access  to  a  clock. 

I.  Bend  the  styles  attached  to  the  fork  and  to  the  pen- 
dulum of  the  tracing  apparatus,  so  that  each  may  graze 
lightly  the  surface  of  a  piece  of  glass.  Powder  the  glass 
with  chalk,  and  set  the  pendulum  in  vibration  by  drawing 
it  about  one  inch  to  one  side  and  releasing  it,  and  set  the 
fork  in  vibration  with  a  sharp  blow  of  a  rubber  hammer. 
Without  loss  of  time,  draw  the  glass  under  the  tracing  ap- 
paratus at  the  rate  of  about  one  foot  per  second. 

Eepeat  until  both  the  fork  and  the  pendulum  have  made 
simultaneous  markings  upon  the  powdered  glass.  The 
pendulum  should  have  registered  at  least  two  complete 
vibrations. 

Measure  the  distance  between  the  two  styles,  and  lay  off 
an  equal  distance  on  one  side  of  each  mark  made  by  the 
pendulum  to  show  points  where  the  pendulum  WOULD  HAVE 
MARKED  if  the  style  attached  to  it  had  absolutely  coincided 
with  that  attached  to  the  fork.  Mark  these  points  a,  b,  c, 
d,  etc. 

Count  the  number  of  complete  waves  traced  by  the  fork 
between  a  and  b,  b  and  c,  c  and  d,  etc.  Estimate  halves, 
and  if  possible  quarters  of  complete  vibrations  in  each  case. 

Time  100  or,  if  possible,  200  complete  vibrations  of  the 
pendulum. 

Are  the  numbers  of  complete  vibrations  between  a  and  b, 
b  and  c,  c  and  d,  etc.,  equal  or  alternately  greater  or  less  ? 
How  do  the  numbers  of  vibrations  between  alternate  marks, 
such  as  a  and  c,  b  and  d,  etc.,  compare?  Why  do  you  prefer 
to  base  calculations  upon  the  number  of  vibrations  registered 


72  GRAPHICAL  MEASUREMENT  OF  PITCH.  [38 

between  alternate  marks?  Why  does  not  irregularity  in 
the  speed  of  the  glass  affect  the  results? 

Calculate  the  number  of  complete  vibrations  made  by  the 
fork  in  one  second.  What  name  is  given  to  this  quantity  ? 

II.  Repeat  this  experiment  from  the  beginning  until 
concordant  results  are  obtained.  Find  out  whether  the  arc 
of  oscillation  of  the  pendulum  has  any  appreciable  effect 
upon  its  rate  of  vibration,  and  whether  the  amplitude  of  the 
tuning  fork  affects  the  results* 


39]  BREAKING  STRENGTH.  73 


39.    BREAKING    STKENGTH. 

APPARATUS:  A  spring  balance  of  30  Ibs.  capacity; 
standard  weights  for  testing  the  same;  two  bobbins,  one 
fixed,  the  other  attached  to  the  hook  of  the  balance;  several 
lengths  of  wire  about  one  metre  each;  a  metre  rod;  access  to 
scales  with  weights  to  0.1  gram;  access  to  screw  gauge. 

I.  Find  the  reading  of  a  spring  balance,  when  unloaded, 
both  in  a  vertical  and  in  a  horizontal  position. 

Does  the  spring  balance  read  the  same  in  these  two 
positions  and  why  ? 

How  should  the  spring  balance  be  held  to  avoid  cor- 
rections from  this  source  ? 

II.  Test  the  spring  balance  by  hanging  weights  on  it — 
say  10,  20,  and  30  Ibs.      Within  what  probable  limits  can 
the  balance  be  assumed  to  be  accurate? 

III.  Cut  off  a  metre  of  fine  copper  wire  (No.  31,  B.W.G.), 
and  weigh  it  to  0.1  gram. 

Find  the  diameter  of  the  wire,  by  a  screw  gauge,  within 
0.001  cm.  Ask  for  instructions  if  necessary  in  the  use  of 
the  gauge. 

Fasten  one  end  of  the  wire  to  a  fixed  bobbin,  and  wind 
most  of  it  round  the  bobbin.  Fasten  the  other  end  of  the 
wire  to  a  spring  balance,  and  take  one  or  two  turns  round 
a  bobbin  attached  to  the  hook  of  the  balance. 

Apply  a  steadily  increasing  force  to  the  wire.  Notice  the 
indication  of  the  spring  balance  when  the  wire  begins  to> 
stretch,  also  when  the  wire  breaks.  TAKE  GARE  that  the 
hand  is  held  so  as  not  to  be  injured  by  the  recoil  of  the 
spring. 

Measure  the  diameter  of  the  wire  near  the  break. 

Repeat  until  tolerably  concordant  results  are  obtained. 


74  BREAKING   STRENGTH.  [39 

IV.  Kepeat  III.  with  a  brass  or  steel  wire  of  as  nearly 
as  possible  the  same  diameter. 

V.  Repeat  IY.  with  a  wire  of  the  same  material,  but  of 
either  twice  the  cross-section,  or  twice  the  diameter. 

YI.     Answer  the  following  questions: — 

1.  How  do  the  different  wires  experimented  with  com- 
pare in  respect  to  stretching  before  breaking?  and  as  to  the 
contraction  of  their  diameter  near  the  break? 

2.  Find  the  relative  breaking  strength   of  wires   of  at 
least  two  different  materials,  having  the  same  cross-section. 

3.  Calculate  the  length  of  each  wire  which  would  break 
under  its  own  weight. 

Why  should  the  last  result  be   the   same   for   any  two 
wires  of  the  same  material? 

4.  Find  the  cross-section  of  each  wire   (by  multiplying 
the  square  of  its  diameter  by  0.7854),  and  calculate  the  force 
in  metric  "tonnes"      (1000  kilos.  =2205  Ibs.  to  the  "tonne") 
necessary  to  break  a  wire  of  the  same  material  one  sq.  cm. 
in    cross-section,  assuming  that  the  breaking   strength   is 
proportional  to  the  cross-section. 


40]  STRETCHING  WIRES.  75 


40.    STRETCHING  WIRES. 

APPARATUS:  A  30-lb.  spring  balance;  a  metre  rod  divided 
into  millimetres;  considerable  lengths  (from  4  to  10  metres) 
of  wires  of  different  diameters  and  materials;  screw  hooks 
for  fastening  the  same;  access  to  a  screw  gauge. 

I.  Fasten  one  end  of  a  small  wire  to  a  screw  hook  (or 
vice),  the  other  end  to  the  hook  of  a  30-lb.  spring  balance. 
Bend  the  loose  end  of  the  wire  near  the  spring  balance  at 
right  angles  with  the  main  portion  of  the  wire,  so  as  to 
form  an  index,  by  which  the  elongations  of  the  wire  are 
to  be  read.  Fix  a  scale  of  millimetres  so  as  to  measure 
the  elongations  in  question. 

Straighten  the  wire  by  a  strain  of  two  or  three  pounds, 
and  gradually  increase  the  force  until  the  index  comes  ex- 
actly opposite  one  of  the  mm.  divisions  on  the  scale.  Note 
this  mm.  division,  also  the  reading  of  the  spring  balance. 

Again  increase  the  force  until  the  wire  stretches  another 
mm.  Note  the  reading  of  the  index  on  the  mm.  scale,  and 
that  of  the  spring  balance  as  before. 

Continue  in  this  way  until  the  force  reaches  one  third  the 
breaking  strength  of  the  wire,  or  if  this  be  unknown,  until 
the  wire  has  stretched  one  thousandth  part  of  its  length. 
Do  not  apply  greater  forces,  for  fear  of  exceeding  the  limits 
of  perfect  elasticity  of  the  wire. 

Repeat  until  concordant  results  are  obtained.  Always 
record  the  WHOLE  readings,  thus  : 

Index        653  mm.         Force        3.5  Ibs. 
654mm.  "  5.7  Ibs. 

etc.  etc. 

Do  NOT  record  the  DIFFERENCES  between  successive  read- 
ings, e.  g.  "1  mm.,  2.2  Ibs."  The  former  method  contains 
all  the  information  that  the  latter  contains,  and  more. 


76  STRETCHING  WIRES.  [40 

II.  Kepeat  I.  with  an  index  attached  to  the  middle  of 
the  wire,  so  that  the  stretching  of  only  half  is  measured. 

III.  Repeat  I.  with  a  larger  wire  of  the  same  material 
and  length. 

IY.  Eepeat  I.  with  a  wire  of  as  nearly  as  possible  the 
same  length  and  diameter,  but  of  different  material  (e.  g. 
copper). 

V.  Substitute   in  IY.,   if  time  permits,  other  wires   of 
different  materials. 

VI.  Find  the  length  of  all  the  wires  subject  to  stretching, 
by  the  metre  scale;  also  the  diameter  of  these  wires,  as  in 
Experiment  9,  by  a  screw  gauge. 

1.  How  does  the  increase    of  force  compare  in  general 
with  the  increase  of  stretching?     Why  is  it  necessary  to  be- 
gin with  a  certain  force  in  order  that  regularity  in  this  com- 
parison may  appear?     Why  is   it  unnecessary   to  apply  a 
correction  for  the  position  of  the  spring  balance? 

2.  How   does   the   force   required   to  produce   a  given 
amount    of  stretching  vary    with    the    length   subject  to 
stretching? 

3.  How   does   the  force  required  to   produce   a  given 
amount  of  stretching  vary  with  the  diameter  of  the  wire  ? 
with  the  cross-section  of  the  wire? 

4.  Find  the  force  in  grams  (453.6  grams  to  the  Ib.  Avoir- 
dupois) which  would  double  the  length  of  a  wire  1  sq.  cm. 
in  cross-section,  provided  that  rupture  did  not  take  place. 
Note  that  this  is  called  "Young's  modulus  of  elasticity ,w    Is 
Young's  modulus  the  same  for  all  materials? 


41]  BENDING  BEAMS.  77 


41.    BENDING  BEAMS. 

APPARATUS  :  Two  knife-edges  ;  a  scale-pan  with  suspend- 
ing cord ;  three  beams,  more  than  one  metre  long,  1  by  1, 
1  by  2,  and  2  by  2  cm.  ;  two  weights,  500  g.  and  1000  g. ; 
a  metre  rod. 

I.  Support   a  wooden  beam,   one  cm.    square,   on  two 
knife-edges,  100  cm.  apart ;  hang  a  scale-pan  from  the  mid- 
dle of  the  beam,  by  a  cord  passing  through  a  hole  in  the 
table ;    and   note   the   height   of  the   middle   of  the  beam 
above   the  table,   as   measured  by  a  vertical   scale  of  mm. 
sighted  across  the  upper  surface  of  the  beam. 

Place  a  500-gram  weight  in  the  pan,  and  again  determine 
the  height  of  the  beam.  How  much  has  the  beam  been  de- 
flected by  the  weight  ? 

II.  Eepeat  I.  with  1000-gram  weight.      How   does  the 
deflection  due  to  1000  grams  compare  with  that  due  to  500 
grams  ? 

III.  Find  as   in  I.   the  deflection  due  to  1500  grams. — 
Find  by  comparison   of  the   weights  and   deflections  in  I., 
II.,   and  III.,   the    simplest   possible   law  connecting   the 
deflection  with   the  weight,   within  the   limits   of  errors  of 
observation. 

IV.  Eepeat  III.   with  a  beam  1  cm.  by  2  cm.  in  cross- 
section,  laid  flatwise   on  the    supports.       How   does   the 
breadth   of  the   beam   in  IV.,   compare   with  that  in  III.  ? 
How  do  the  lengths,  depths,  and  weights  compare  in  III, 
and  IV.  ?      What  is  the   effect  of  doubling  the   breadth   of 
the  beam  on  the  deflection  produced  ? 

V.  Bepeat  IV.  with  the  beam  edgewise.      What  is  the 
effect  of  doubling  the  depth  of  the  beam  on  the  deflection 
produced? 

VI.  Bepeat  V.  with  a  beam  2  cm.  by  2  cm.      Find  by 


78  BENDING  BEAMS.  [41 

comparison  of  the  results  in  V.  and  VI.  the  effect  of  doub- 
ling the  breadth  of  a  beam,  2  cm.  deep.  Find  by  com- 
parison of  the  results  in  IV.  and  VI.  the  effect  of  doubling 
the  depth  of  a  beam  2  cm.  broad.  Find  by  comparison  of 
III.  and  VI.  the  effect  of  doubling  the  diameter  of  a  square 
beam. 

How  do  your  inferences  in  VI.  as  to  the  effects  of  doubling 
the  breadth  and  depth  of  a  beam  compare  with  those  in  IV. 
and  V.?  Assuming  that  the  deflection  of  a  beam  is  pro- 
portional directly  or  inversely  to  some  power  of  the 
breadth,  to  some  power  of  the  depth,  and  to  some  power  of 
the  mean  diameter  (if  the  shape  of  the  cross-section  is  con- 
stant), what  are  the  powers  in  question? 

VII.  Kepeat  III.  with  a  distance  of  50  cm.  instead  of  100 
cm.  between  the  supports.  If  the  deflection  of  a  beam  is 
proportional  to  some  integral  power  of  its  length,  what  is 
the  power  in  question? 

State  the  laws  connecting  the  deflection  of  a  beam  with 
its  length,  breadth,  depth,  and  load  suggested  by  your  ex- 
periments. 

Express  the  load  upon  a  beam  in  terms  of  some  constant 
multiplied  by  integral  powers  of  the  length,  breadth, 
depth,  and  deflection  of  the  beam,  assuming  the  laws  above 
to  be  true. 


42]  TWISTING    EODS.  79 


42.    TWISTING  KODS. 

APPARATUS:  A  single  piece  for  from  2  to  4  students,  con- 
sisting of  the  following  parts:  2  beams,  1  by  1  and  2  by  2 
cm.,  respectively,  each  115  cm.  long;  a  clamp  (with  spirit 
level)  joining  the  beams  together  horizontally;  two  sockets, 
with  cardboard  circles  for  the  free  ends;  centres  to  support 
the  same;  4  bobbins,  5  cm.  long,  5  cm.  diameter,  fitting  the 
rods;  4  spring  balances  (4  Ibs.  by  oz.);  jacks  on  rollers  to 
support  spring  balances  horizontally;  cords  to  connect 
balances  with  bobbins;  and  means  of  shortening  the  same. 
A  metre  rod,  and  access  to  a  vernier  gauge. 

I.  Attach  one  pair  of  spring  balances  to  the  middle  bob- 
bin on  the  small  beam,  the  other  pair  to  the  middle  bobbin 
of  the  larger  beam;  but  put  no  strain  on  them.        See  if  the 
circles  both  read  zero  when  the  clamp  is  leveled.     If  not, 
note  the  reading  of  each  circle. 

Tighten  one  of  the  cords  until  the  spring  balances  read 
64  oz.  Why  do  all  the  spring  balances  give  the  same  read- 
ing? 

Readjust  the  level  on  the  clamp,  and  note  the  angle  of 
twist  in  each  beam.  If  the  twist  is  proportional,  directly 
or  inversely,  to  some  power  of  the  diameter,  what  is  the 
power  in  question? 

II.  Repeat  I.  with  the  balances  attached  to  the  outer 
bobbin  in  each  case. 

How  does  the  twist  of  a  beam  compare  with  the  length 
subject  to  torsion  ? 

III.  Eepeat  II.  with  forces  of  32  oz.  instead   of  64  oz. 
How  does  the  twist  of  a  beam  compare  with  the  forces  ap- 
plied to  it  under  given  conditions? 

In  what  respects  do  the  laws  of  torsion  correspond  with 


80  TWISTING    BODS.  [42 

the  laws  of  stretching,  and  in  what  respects  do  the  ycorre- 
spond  with  laws  of  bending  ? 

State  a  general  law  (Hooke's  law)  connecting  force  with 
the  displacement  produced  (whether  longitudinal,  trans- 
verse, or  torsional).  See  Exps.  40 — 42. 

Show  that  the  relation  between  the  length  of  a  beam, 
subject  to  stretching  or  torsion,  and  the  angle  of  torsion 
produced  could  be  anticipated  by  arithmetical  con- 
siderations. 


43]  COUPLES.  81 


43.     COUPLES. 

APPARATUS:  A  torsion  apparatus;  a  screw-driver;  2  spring 
balances,  (4  Ibs.  by  oz.);  strings  and  screw-eyes  for  attach- 
ing the  same;  a  metre  rod. 

I.  Bead  the  disc  of  the  torsion  apparatus  by  two  nails 
on  opposite  sides  of  the  disc.     Place  one  of  the  movable 
pegs  opposite  the  point  i,   of  the   disc,  and  connect  it,  by 
means  of  a  spring  balance  and  cords,  to  a  screw-eye  at  j. 
Place  the  other  peg  similarly  opposite  j,  and  connect  it,  by 
the  other  spring  balance,  with  the  screw-eye  at  i.     Tighten 
the  cords  by  twisting  the  pegs  equally,  until  each    spring 
balance  reads  36  ounces.     Slide  the*  pegs  until  tlie  cords  are 
at  right-angles   with   ij,  and   readjust   the   tension   to   36 
ounces.     Read  the  disc  by  means  of  the    two  fixed    nails. 
Measure   the   perpendicular   distance   between  the   cords. 
Note  whether  the  disc  is  deflected  bodily,  or  only  twisted 
about  its  centre. 

II.  Repeat  I.  with  d  and  e  substituted  for  i  and^'. 

III.  Repeat  II.  with  b  substituted  for  e,  but  with  forces 
unchanged  in  direction,  and  hence  at  right-angles  with  c  e, 
(not  b  d).  4 

IV.  Repeat  II.  with  a  and  b  substituted  for  d  and  e,  and 
forces  unchanged  in  direction,  that  is,  at  right-angles  with 
a  b  or  c  e. 

V.  Repeat  II.  with  c  and  d  substituted  for  d  and  e,  and 
forces   unchanged  in  general   direction,  that   is,  at   right- 
angles  with  c  d. 

VI.  Repeat  II.  with  12  ounces  for  36  ounces,  and  c  and  / 
for  d  and  e. 

VII.  Repeat  VI.  with  c  and  e  for  c  and  /. 

VIII.  Repeat  VI.  with  d  and  e  for  c  and/. 

IX.  Tabulate  results  as  follows:  column  1,  numbers  cor- 
responding to  parts  I. — VIII.  of  this  experiment;  column  2, 
forces  in  ounces  applied;  column  3,  perpendicular  distances 
between  cords;  column  4,  products  of  numbers  in  columns  2 

6 


82  COUPLES.  [43 

and  3;  column   5,  deflections   in   cm.  produced;   column   6, 
ratios  of  numbers  in  columns  4  and  5. 
Answer  the  following  questions: 

1.  What  is  the  effect  of  rotating  a  "couple"   from  the 
symmetrical   position,  ij,  in   I.,   through   a   certain   angle, 
(90  ° )   into   another   symmetrical   position,  d  e   in  II,  the 
magnitude  of  the  forces  and  perpendicular  distance  between 
the  cords  remaining  the  same  ? 

2.  What  is  the  effect  of  changing  the  point  of  applica- 
tion of  one  of  the  forces  from  e  in  II.,  to  b  in  III.,  the  lines 
of  action  of  the  forces,  and  hence  the   perpendicular   dis- 
tance between  them,  remaining  unchanged? 

3.  What  is  the  effect  of  moving   a   "couple"   from   the 
symmetrical   position,  d  e,  in  II.,  in   a   direction   at  right- 
angles  to  d  e,  into  the  unsymmetrical  position,  a  b,  in  IV.  ? 

4.  What  is  the  effect  of  moving   a   "couple"    from   the 
symmetrical  position,  d  e,  in  II.,  in  a  direction  parallel   to 
d  e,  into  the  unsymmetrical  position,  c  d,  in  V.? 

5.  What  in  general  would  you  infer  to  be  the  effect  of 
moving  a  "couple"  from  one  place  to  another  without  chang- 
ing the  magnitude  of  the  forces  or  the  perpendicular  dis- 
tance between  their  lines  of  a  action  ? 

6.  What  is  the  effect  of  increasing   the   perpendicular 
distance  between  $he  lines  of  action  of  two  forces,  constitu- 
ting a  "couple,"  from  9  cm.  in  II.,  to  27  cm.  in  VI.,  provided 
that  the  forces  are  diminished  in  the  same  •  proportion,  so 
that  the  product  of  the  forces  and  the  perpendicular  dis- 
tances between  their  lines  of  action  remains  the  same  ? 

7.  What  is  the  effect  of  varying  the  perpendicular  dis- 
tance between  the  lines  of  action  of  two   constant  forces 
constituting   a   "couple"   on  the   angle  of  twist  produced? 
(See  VI.,  VII,  VEIL) 

8.  What  is  the  effect  of  changing  the  force  from  36  oz. 
in  II.  to  12  oz.  in  VIII? 

9.  Name  all  the  circumstances  discovered  in  this  and  in 
the  last  experiment  which  may  modify  the  angle  of  torsion 
produced  in  a  rod  of  given  length  and  diameter. 

10.  Upon  what  product  does  the    effect  of    a    couple 
depend  ? 


44]  COMPOSITION  OF  FORCES.  83 


44.    COMPOSITION  OF  FOECES. 

APPARATUS:  A  blackboard;  two  30-lb.  spring  balances*, 
hooks  for  supporting  the  same;  6  metres  of  strong  cord;  a 
weight  over  30  Ibs;  a  lever;  a  metre  rod;  and  chalk. 

I.  Suspend  a  horizontal  lever  by  means  of  two  vertical 
cords  attached  to  two  spring  balances,  hung  upon  stout 
nails  or  hooks  at  the  proper  distance.  Bead  the  spring 
balances.  Attach  the  weight  by  a  cord  between  the  middle 
and  end  of  the  lever,  and  again  read  the  spring  balances. 
Measure  the  distances  between  the  middle  cord  and  the  ex- 
treme cords. 

Answer  the  following  questions: 

1.  What  two  couples,  introduced  by  the  suspension  of 
the  weight,  are  in  equilibrium? 

2.  What  relation   exists  between   the   increase   in  the 
reading  of  each  spring  balance  and  the  distance  of  its  cord 
from  the  middle  cord  ?  and  why  ? 

3.  What  is  the  magnitude  of  the  weight   (that   is,  how 
many  pounds  does  it  weigh)  ?      Give  reasons  in  full  for  this 
answer. 

II.  Repeat  I.  with  the  weight  suspended  at  the  centre  of 
the  lever.     Answer  questions  1,  2,  and  3,  under  I. 

III.  Hang  up  two  spring  balances  of  30  Ibs.  capacity  on 
two  nails  above  a  blackboard,  at  a  distance  of  about  one 
metre.     Connect  these  by  a   cord  a  little  over  a  metre  in 
length.     From  the  middle  of  the  cord,  suspend  a  weight  of 
a  little  over  30  Ibs.      Draw  lines  on  the  blackboard  parallel 
to  the  three  sections  of  the  cord.     Measure  off,  on  two  of 
these  lines,  distances  in  inches  numerically  equal  to  the  re- 
spective forces  in  Ibs.  indicated  by  the  spring  balances  act- 
ing  along  these  lines.      Complete  the  parallelogram  with 
these  distances  as  sides.       Draw  the  diagonal  of  this  paral- 


84  COMPOSITION    OF  FORCES.  [44 

lelogram,  and  measure  it  in  inches.       Answer  the  following 
questions: 

1.  What   relation   exists  between   the   direction  of   the 
diagonal  and  that  of  the  cord  supporting  the  weight?  and 
why? 

2.  What  relation  exists  between  the  sides  of  the  paral- 
lelogram? and  why? 

3.  What  is  the  magnitude  of  the  weight,  and  why? 

IV.  Move  the  point  of  attachment  of  the  weight  so  as  to 
be  nearer  one  spring  balance  than  the  other,  then  proceed 
as  in  III.  Answer  questions  1,  2,  and  3,  under  III. 

Y.  Hang  up  the  weight  by  a  long  cord  from  one  of  the 
nails.  Lay  a  scale  of  inches  horizontally  on  the  ledge  of  the 
blackboard.  Pull  the  weight  sideways  (horizontally)  by 
means  of  a  spring  balance,  until  the  deflection  of  the  sus- 
pending cord,  measured  by  the  scale,  amounts  to  one  foot ; 
then  read  the  spring  balance.  Measure  the  vertical  dis- 
tance from  the  nail  to  the  scale. 

Calculate  the  weight  by  the  triangle  of  forces. 

VI.  Eepeat  V.  with  a  deflection  of  2  feet  instead  of  1  ft. 
Calculate  the  weight  as  in  V. 

VII.  Make   a   table   showing  the  different  estimates  of 
weight  in  I. — VI.,  and  answer  the  following  questions: 

1.  Why  could  not  the  weight  be  directly  measured  by 
suspension  from  a  single  one  of  the  spring  balances  ? 

2.  How   do  you  explain  the   differences   between   your 
different  estimates  of  the  weight? 

3.  What  are  your  inferences  as  to  the  relative  accuracy 
and  utility  of  the  different  methods  employed  for  the  esti- 
mation of  weight  by  the  composition  of  forces  ? 


45]  FALLING  BODIES.  85 


45.    FALLING  BODIES. 

APPARATUS:  A  falling  bodies'  apparatus,  with  ball, 
thread,  carbon  paper  and  matches;  trip  scales  with  weights 
to  1  gram,  and  a  spring  balance,  graduated  in  decimal  mul- 
tiples of  a  dyne. 

I.  Attach  a  strip  of  white  paper,  and  over  it,  a  strip  of 
carbon  paper,  near  the  lower  end  of  a  pendulum  rod,  and 
hang  up  a  ball  by  a  thread  passing  over  a  peg  above  the 
rod,  so  that  the  ball  may  hang  opposite  the  papers.  Slide 
the  support  of  the  pendulum  rod,  if  necessary,  so  as  to 
graze  the  ball  when  at  rest. 

Raise  the  ball,  by  the  thread,  to  a  mark  near  the  top  of 
the  pendulum  rod;  pass  the  thread  around  the  three  pegs, 
and  fasten  it  to  a  screw-eye  in  the  pendulum  rod.  Adjust 
the  length  of  the  thread  so  that  the  pendulum  may  be  de- 
flected ten  or  twenty  degrees,  while  the  ball  hangs  opposite 
the  mark  near  the  top  of  the  rod.  Be  sure  that  the  ball  and 
pendulum  are  about  in  equilibrium,  so  that  a  slight  jar  may 
not  disturb  the  adjustment. 

Stop  all  oscillation  of  the  ball,  and  burn  the  thread  be- 
tween the  two  upper  pegs.  The  ball  in  falling  should 
strike  the  strips  of  paper,  and  make  a  mark  on  the  white 
paper.  Readjust  the  papers,  if  necessary,  until  this  result 
is  attained. 

Measure  the  distance  between  the  mark  at  the  top  of  the 
pendulum  rod,  where  the  ball  began  to  fall,  and  that  made 
by  the  ball  on  the  white  paper.  Repeat  until  two  or  three 
concordant  results  are  obtained.  (They  should  not  differ 
by  more  than  1  cm.) 

Find  the  time  of  the  pendulum,  by  observations  of  100 


86  FALLING  BODIES.  [45 

complete  oscillations;*  and  calculate  the  time  occupied  in 
reaching  the  middle  point  of  the  first  half-swing,  where  the 
ball  and  pendulum  meet. 

"What  is  the  distance  fallen  in  the  given  time?  "What  is 
the  mean  velocity  during  this  time  ?  What  is  the  final  ve- 
locity? (This  may  be  assumed  to  be  twice  the  mean  veloc- 
ity, since  the  initial  velocity  is  zero). 

II.  Repeat  I.  with  one  or  more  pendulum  rods  of  differ- 
ent lengths. 

Answer  the  following  questions: 

1.  If  the  distance  through  which  a  body  falls  in  a  given 
time  is  proportional  to  .some  integral  power  of  this  time, 
what  is  the  power  in  question  ? 

2.  If  the   average   velocity   of  a   falling  body   is   pro- 
portional to  some  integral  power  of  the  time  of  fall,  what  is 
the  power  in  question? 

3.  Show  that  your  answers  to  (1)  and  (2)  are  consistent, 
remembering  that  the   distance   traversed   by  any  moving 
body  in  a  given  time  is  equal  to  the  product  of  that  time 
and  the  average  velocity. 

4.  If  the  final  velocity  of  a  falling  body  (originally  at 
rest)  is  always  twice  its  average  velocity,   what  law   con- 
nects the  final  velocity  with  the  time  of  fall? 

5.  What  velocity  would  the  body  experimented  upon  ac- 
quire in  ONE  SECOND,  assuming  the  law  in  (4)  to  be  true? 

6.  How  do  bodies  differing  in  mass  or  in  material  com- 
pare in  regard  to  the  velocity  which  they  acquire  in  a  given 
time  under  the  action  of  the  earth's  gravity,  when  frictional 
forces,  due   to  the  air  or  other  causes,  can  be  neglected? 
(Ask,  if  necessary,  for  directions  enabling  you   to   answer 
this  question  experimentally). 

III.  Find  by  a  balance  the  weight  in  grams  (or  mass)  of 
the  falling  body.       Find  also  by  means  of  a  spring  balance, 
as  in  Exp.  1,  its  weight  in  dynes. 


*  A  "complete  oscillation"  of  a  pendulum  consists  of  two  swings  in  oppo- 
site directions  ;  one  from  the  farthest  left-hand  point  to  the  farthest  right-hand 
point,  the  other  from  the  farthest  right-hand  point  back  again  to  the  farthest 
left-hand  point.  The  "time"  of  a  pendulum  is  that  occupied  by  a  single  swing 
in  either  direction — that  is,  by  one  half  of  a  complete  oscillation. 


45]  FALLING  BODIES.  87 

Multiply  the  mass  of  blie  falling  body  by  the  velocity 
which  it  acquires  in  one  second.  (See  (5)  under  II.)  How 
does  this  product  compare  with  its  weight  in  dynes? 

Assuming  that  the  weight  of  a  body  in  dynes  is  numeri- 
cally equal  to  the  product  of  its  mass  and  velocity  acquired 
per  unit  of  time  under  the  action  of  gravity,  what  is  the 
WEIGHT  OF  ONE  GRAM  IN  DYNES?  Compare  this  result  with 
that  obtained  in  Exp.  1. 


88  MAGNETIC  ATTRACTIONS  AND   REPULSIONS.  [46 


46.    MAGNETIC  ATTKACTIONS  AND  REPULSIONS. 

APPARATUS:  Three  magnets,  about  15  X  1.2  X  .6  cm.; 
2  unmagnetized  bars  of  the  same  dimensions;  a  balance  sen- 
sitive to  leg.;  a  set  of  dyne-weights;  lead  shot  for  counter- 
poising; a  stand  to  hold  a  magnet  ;  a  metre  rod. 

NOTE.  The  magnets  are  supposed  to  be  horizontal  and 
to  lie  flatwise  throughout  these  experiments. 

I.  Place  magnet  No.  3  on  the  balance  pan;  counterpoise 
it,  and  raise  the  balance  beam  by  its  lever,  so  that  the  mag- 
net may  swing  freely. 

Find  whether  the  poles  of  two  other  magnets  marked  "N"~ 
attract  or  repel  that  of  the  suspended  magnet  marked  in  the 
same  way,  when  held  at  a  short  distance  (2  or  3  cm.)  from 
it;  find  also  how  they  act  upon  the  pole  marked  "S";  find 
also  how  the  poles  marked  "S"  act  upon  each  pole  of  the 
suspended  magnet. 

Which  poles  of  the  two  magnets  not  suspended  are 
similar,  and  which  dissimilar,  in  respect  to  their  action  up- 
on the  poles  of  the  suspended  magnet? 

II.  Find  whether  two  poles  found  in  I.  to  be  similar  at- 
tract or  repel  each  other;  also  whether  two  dissimilar  poles 
attract  or  repel  each  other. 

III.  Counterpoise    magnet  No.  1   on  the  balance,  and 
clamp  magnet  No.  2  so  that  one  of  its  poles  may  be  directly 
above  the  similar  pole  of  No.  1.     Make  the  distance  between 
the  axes  of  the  magnets  exactly  2  cm.  when  the  balance 
beam    is    raised    and    horizontal.       Slide   the   stand,    to 
which  magnet  No.  2  is  clamped,  over  the  table,  so   as    to 
change  the  distance  by  which  the  two  poles  overlap  WITH- 
OUT CHANGING  THE  DISTANCE  BETWEEN  THE  AXES  OF  THE  MAG- 


46]  MAGNETIC  ATTRACTIONS  AND   REPULSIONS.  89 

NETS.     Find  a  position,  in  this  way,  in  which  a  maximum 
repulsion  is  obtained. 

Assuming  that  the  poles  of  the  two  magnets  are  similarly 
situated,  and  that  their  mutual  repulsion  is  some  function 
of  the  distance  between  them,  where  are  these  poles 
located?  Multiply  experiments  until  you  feel  sure  of  your 
answer. 

IV.  Measure  the  force  in  dynes  with  which  a  single  pair 
of  similar  poles  repel  each  other  under  the  conditions  of 
III.     Do  this  by  the  use  of  dyne-weights  (i.  e.  weights  so 
adjusted  that  the  force  in  dynes  exerted  by  gravity  upon 
them   at  Berkeley   is   correctly  indicated   by   the  numbers 
stamped  upon  the  weights). 

V.  Place  the  centre  of  magnet  No.  2  directly  above  the 
centre  of  magnet  No.  1,  and  at  a  distance  of  2  cm.  from  it, 
as  in  III.     Then  rotate  magnet  No.  2  until  a  maximum  of 
repulsion  is  observed. 

Describe  the  relative  position  of  the  magnets  and  of  their 
poles  when  this  occurs.  . 

YI.  Make  sure  that  the  distance  between  the  two  mag- 
nets is  still  2  cm.  from  centre  to  centre.  Measure  the  force 
of  repulsion  between  the  two  magnets  as  in  IV.,  by  the  use 
of  dyne-weights. 

How  does  this  compare  with  the  force  exerted  in  III.  by 
a  single  pair  of  poles?  and  why? 

VII.  Repeat  VI.  with  magnet  No.  3  instead  of  No.  2. 

VIII.  Repeat  VII.  with  magnet  No.  2  instead  of  No.  1. 

IX.  Select  from  your  three  magnets  a  pair  as  nearly  as 
possible  equal  in  strength;  set  them  up  as  in  VI.,  VII.,  or 
VIII.,  only  turn  one  of  them  end  for  end,  so  as  to  produce 
attraction  instead  of  repulsion,  and  measure  this  attraction, 
at  a  mean  distance  of  2  cm.  as  before,  by  the  use  of  dyne- 
weights. 

Is  the  repulsion  between  two  magnets  at  a  given  (small) 
distance  equal  to,  greater  than,  or  less  than  the  attraction? 

X.  Take  a  bar  of  uumagnetized  steel  (make  sure  that  it 
is  unmagnetized,  by  proving  that  it  has  no  attraction  or  re- 
pulsion for  a  similar  bar),  and  measure  the  force  in  dynes 


DO  MAGNETIC  ATTRACT  ONS  AND   REPULSIONS.  [46 

with  which  it  attracts  or  is  attracted  by  one  of  the  steel  mag- 
nets already  employed,  when  held  at  a  distance  of  2  cm. 
from  this  magnet.  Find,  also,  the  effect  of  turning  the  mag- 
net end  for  end. 

Under  what  circumstances  (if  any)  is  a  piece  of  unmag- 
netized  steel  repelled  by  a  magnet? 

"What  should  you  suppose  to  be  the  action  between  either 
of  two  magnets  and  the  unmagnetized  portion  of  the  steel 
of  which  the  other  magnet  is  composed  ? 

Account  (quantitatively,  if  possible)  for  the  difference  be- 
tween the  attractive  and  repulsive  forces  of  two  magnets  at 
a  given  distance. 

XL  Repeat  IX.  with  a  distance  of  1  cm.  instead  of  2  cm. 
between  the  centres  of  the  magnets,  so  as  to  find  the  force 
of  attraction  with  a  distance  of  1  cm.  between  each  pair  of 
poles.  Then  reverse  one  of  the  magnets,  and  find,  as  in  VI.r 
VII.,  or  VIII.,  the  force  of  repulsion  under  similar  circum- 
stances. Divide  each  of  these  results  by  2,  to  find  the  force 
due  to  a  single  pair  of  poles.  Average  the  two  quotients  to 
find  the  mean  force  (whether  attractive  or  repulsive)  be- 
tween a  single  pair  of  poles  at  a  distance  of  1  cm. 

Why  is  the  so-called  "inductive  effect,"  studied  in  X., 
eliminated  by  thus  taking  an  average  ? 

Assuming  that  the  mean  force  in  dynes  between  the  two 
poles  in  question,  at  the  distance  of  1  cm.  (being  equal  in 
general  to  the  product  of  the  numbers  of  units  of  magnetism 
which  they  contain)  is  in  this  case  (the  poles  being  equal  in 
strength)  equal  to  the  square  of  the  number  of  units  in 
each,  calculate  the  strength  of  either  pole  in  magnetic 
units. 

XII.  Calculate  as  in  XL,  from  the  results  of  VI. — IX., 
the  mean  attractive  and  repulsive  force  between  a  single 
pair  of  poles  2  cm.  apart. 

If  the  mutual  attraction  or  repulsion  of  two  poles  varies, 
directly  or  inversely,  according  to  some  integral  power  of 
the  distance  between  them,  what  is  the  power  in  question? 

Find,  if  time  permits,  whether  the  law  stated  above  seems 


46]  MAGNETIC  ATTRACTIONS  AND   REPULSIONS.  91 

to  hold  for  distances  as  great  as  10  cm.     When  you  have 
decided  as  to  this  fact,  ask  for  an  explanation. 

NOTE.  The  calculations  in  XI.  and  XII.  may  be  deferred, 
if  necessary,  to  the  beginning  of  Exp.  47,  with  which  they 
are  closely  connected. 


92 


HORIZONTAL  COMPONENT  OF  THE  EARTH'S  FIELD.  [4T 


47.     HORIZONTAL  COMPONENT  OF  THE  EARTH'S- 

FIELD. 

APPARATUS:    A   magnet  tested  in  Exp.  46;  a  compass;  a 
metre  rod,  and  a  pencil. 

I.  Draw  a  pencil  line  on  the  table  in  the  direction  indi- 
cated by  a  compass  needle.     Place  a  magnet,  tested  in  Exp. 
46,  on  this  pencil  line,  near  the  compass.     Which  pole  of 
the  magnet  must  be  nearer  the  compass  in  order  to  reverse 
it?     How  near  must  the  end  of  the  magnet  be  to  the  centre 
of  the   compass-needle   in   order   that   reversal   may   take 
place  ?  in  order  that  the  compass  may  be  barely  able  to  re- 
cover  its   ordinary   direction?   in  order  that  the    compass 
may  stand  in  neutral  equilibrium  ? 

II.  Eepeat  I.  with  the  magnet  south  of  the  compass. 

III.  Draw  a  pencil  line  on  the  table  at  right-angles  with 
the  ordinary  direction  of  the  compass,  and  lay  the  magnet 
on  this  line,  east  of  the  compass,  and  with  the  north  pole  to 
the  east.    In  what  direction  is  the  compass  deflected?    How 
is  this  deflection  affected  by  an  increase  or  decrease  in  the 
distance  of  the  magnet?     At  what  distance,  measured  be- 
tween the  nearer  end  of  the  magnet  and  the  centre  of  the 
needle,  is  the  deflection  45  degrees? 

IV.  Eepeat  III.  with  the  magnet  turned  end  for  end. 

V.  Repeat  III.  with  the  magnet  west  of  the  compass. 

VI.  Repeat  III.  with  the  magnet  west   of  the  compass 
and  turned  end  for  end. 

VII.  Answer  the  following  questions: 

1.     Is  your  compass-needle  constructed  so  as  to  be  sensi- 
tive to  horizontal,  or  to  vertical  forces,  exerted  upon   the 
poles?     Must  these  forces  be  parallel  to,  or  at  right-angles 
with,  the  axis  of  the  needle  ;  and  must  they  act  in  the  same 


47]  HORIZONTAL  COMPONENT  OF  THE  EARTH'S   FIELD.          93 

•or  in  opposite  directions  upon   the  two  poles  in  order  to 
affect  the  needle? 

2.  "Why  is  the  direction  indicated  by  the  north  (or  north- 
seeking)  end  of  a  compass-needle  the  same  as  that  of  the 
horizontal  component  of  the  force  which  a  magnetic  north 
pole  would  experience   if  situated  near  the  centre    of   the 
compass? 

3.  How   can   you  find   the   direction   of   the  horizontal 
component  of  the  force  exerted  by  the  earth's  magnetism 
upon  a  magnetic  north  pole?  and  by  what  pencil  line  upon 
the  table  is  this  direction  represented  ? 

4.  Asuming   that  the  force  exerted  by  your  magnet  in 
I.  and  II.    upon  a  magnetic   north  pole    at   the    centre  of 
the  compass  would  be  in  equilibrium  with  the  horizontal 
component  of  the  earth's  force  upon  the  same  pole,  what 
mnst  be   the   direction  of    the  former  ?      And  how  is  this 
direction  related  to  that  of  the  axis  of  the  magnet? 

5.  State  the  angular  relation  in  III. — VI.  between  the 
resultant  force  upon  either  pole  of  the  compass-needle,  de- 
termining the  deflection  of  this  needle,  and  the  (horizontal) 
components  of  this  force  due  one  to  the  magnet,  the  other 
to  the  earth;  also  the  angular  relation  between  these  two 
components.         What  relation  must  exist  between  the  mag- 
nitudes of  these  components  in  order  that  the  angular  rela- 
tions above  may  exist? 

6.  How  does  the  magnitude  of  the  force  exerted  by  your 
magnet  in  I.  or  II.  upon  either  pole  of  the  compass-needle 
compare    with   that   exerted  upon  the   same   pole   by  the 
earth's  magnetism?  and  why? 

7.  Why  are  the  distances  of  the  magnet  from  the  com- 
pass approximately  equal  in  I.  and  II.  ?  in  III. — VI.  ?     How 
do  the  distances  in  I.  and  II.  compare  with  those  in  III. 

-VI,  and  why? 

8.  What  reason  have  you  to  think  that  the  forces  exerted 
loj  your  magnet  upon  ANY  magnetic  pole,  at  the  distance  and 
in  the  relative  position  of  I. — VI.,  would  be  equal  in  mag- 
nitude to  that  exerted  upon  the   SAME  POLE  by  the  earth  ? 
Would  these  conclusions  apply  to  a  north  pole  of  UNIT  MAG- 
NITUDE? 


94  HORIZONTAL  COMPONENT  OF  THE  EARTH'S  FIELD.         [47 

9.  Where  are  the  poles  of  your  magnet?  (See  Exp.  46.) 
How  far  is  the  nearer  pole,  on  the  average,  in  I. — VL,  from 
the  centre  of  the  compass-needle  ?      What  is  the  strength  of 
this  pole?  (See  Exp.  46.)        What  force  in  dynes  would  this 
nearer  pole  exert  on  a  unit  pole  at  the  centre  of  the  com- 
pass?    (To  find  this,  divide  the  strength  of  the  pole  by  the 
square  of  its  average  distance). 

Find  in  the  same  way  the  average  force  in  dynes  exerted 
by  the  farther  pole  upon  a  unit  pole  at  the  centre  of  the 
needle.  Is  this  force  in  the  same  direction  or  in  a  direction 
opposite  to  that  due  to  the  nearer  poles. 

Find  the  resultant  of  the  two  forces  calculated  above. 
Should  the  two  forces  be  added  or  subtracted? 

What  is  the  magnitude  of  the  force  in  dynes  which  the 
earth  would  exert  upon  a  unit  magnetic  pole  ? 

10.  Given  that  a  magnetic  field  is  any  portion  of  space 
in  which  magnetic  poles  are  subjected  to  forces,  and  that 
the  strength  of  a  magnetic  field  is  measured  by  the  force 
in  dynes  exerted  upon  a  unit  magnetic  pole  placed  in  the 
field  in  question,  find  the  strength  of  (1)  the  magnetic  field 
due  to  your  magnet  at  a  distance  along  its  axis  equal  to 
that  in  I. — VI.;  also  (2)  that  due  to  the  earth's  magnetism. 
Why  is  the  earth's  magnetic  field  (approximately)  the  same 
at  different  points  not  very  far  apart  ?        (Ask  if  you  do  not 
know.) 

11.  How  many  tenths  of  a  unit  of  magnetism  would  act, 
at  a  distance  of  one   centimetre,  upon  any  magnetic   pole 
(free  to  move  horizontally)  with  a  force  equal  to  that  ex- 
erted by  the  earth  (at  an  enormously  greater  distance)  upon 
the  same  magnetic  pole? 

12.  Explain,  with  actual  figures  obtained  from  your  ob- 
servations, two  significations  which  may  be  attached  to  the 
statement  that  the  horizontal  component  of  the  earth's  mag- 
netic field  is  equal  to tenths  of  a  unit.     (See  10  and  11.) 


48]  EARTH'S  ACTION  ON  SUSPENDED  MAGNET. 


48.    EARTH'S    ACTION    ON   SUSPENDED  MAGNET. 

APPARATUS:  A  bifilar  suspension,  a  magnet  tested  in 
Exps.  46  and  47;  a  metre  rod;  a  cardboard  protractor;  scales 
and  weights  to  1  gram;  access  to  screw  gauge. 

I.  Adjust  a  "bifilar"  suspension  (if  necessary)  so  that  its 
two  threads  are  of  equal  length,  parallel,  and  magnetically 
east  and  west  of  each  other.       Place  the  magnet,  already 
tested  in  Exps.  46  and  47,  on  the  suspended  carriage,  with 
its  north  pole  toward  the  magnetic  east.     Note  the  deflec- 
tion.     Reverse  the  magnet,  and  again  note  the  deflection. 
Find  the  mean  deflection,  in  degrees. 

II.  Find  the  combined  weight  of  the  magnet  and  sus- 
pended carriage.        (It  is  not  necessary  to  take  down  the 
suspension  to  do  this). 

III.  Find  the  (minimum)  distance  between  the  threads 
in  cm.  with  the  screwfgauge.     Be  careful  not  to  push  the 
threads  out  of  place  by  the  teeth  of  the  gauge. 

IV.  Find  the  length  of  the  threads  in  cm.,  by  the  metre 
rod. 

Y.  Calculate  the  weight  in  grams  on  each  thread  (as- 
suming it  to  be  equally  divided  between  the  two),  and  re- 
duce this  to  dynes,  by  the  usual  factor  (980.0  at  Berkeley. 
See  Exps.  1.  and  45). 

VI.  Calculate  the  deflection  of  each  thread  from  the  ver- 
tical.    (This  is  approximately  equal  to  the  half  distance  be- 
tween the  threads  multiplied  by  the  sine  of  the  mean  angle 
of  deflection). 

VII.  Calculate  the  horizontal  component  of  the  force  of 
gravity  exerted  upon  each  thread  (by  multiplying  the  total 
force  in  dynes  by  the  ratio  of  the  deflection  from  the  verti- 
cal to  the  total  length  of  the  thread). 

VIII.  Calculate  the  couple  due  to  the  force  of  gravity. 


$6  EARTH'S  ACTION  ON  SUSPENDED  MAGNET.  [48 

IX.  Knowing,  by  Exp.  46,  the  location  of  the  poles,  find 
the  horizontal  force  in  dynes  on  each  producing  a  couple 
equal  to  that  due  to  gravity. 

X.  Knowing,  by  Exp.  46,  the  strength  of  the  poles   of 
your  magnet,  find  the  (horizontal  component  of  the)  force 
exerted  by  the  earth  upon  each  unit  of  magnetism  which 
these  poles  contain.     What  name  is  given  to  this  last  re- 
sult?    (See  Exp.  47.) 

XI.  Suppose  that  you  had  overestimated  the  strength  of 
your  magnetic  poles  in  Exp.  46,  by  say  100%.      What  error 
would  this  introduce  in  your  estimate   of   the    (horizontal 
component  of  the)  earth's  magnetic  field  in   Exp.    47?   in 
Exp.  48? 

XII.  Account  any  large  difference   between  your   esti- 
mates of  the  (horizontal  component  of  the)  earth's  magnetic 
field  in  Exps.  47  and  48;  and  find  the  geometric  mean  be- 
tween these  two  estimates.     Why  is  this  geometric  mean 
unaffected   by  any  error  in  your  original  estimate   of   the 
strength  of  the  poles  of  your  magnet? 

NOTE.  Students  who  find  difficulty  in  following  out  the 
reductions  of  results  obtained  with  the  "bifilar  suspension" 
will  do  well  to  ask  for  special  instructions  as  to  the  use  of  a 
piece  of  apparatus  by  which  these  difficulties  may  be 
avoided.  The  apparatus  consists,  essentially,  of  a  mechani- 
cal device,  through  which  the  horizontal  force  exerted  by 
the  earth's  magnetism  upon  the  poles  of  a  suspended  mag- 
net may  be  directly  counterpoised  with  weights.  The  use 
-of  a  bent  lever  for  this  purpose  was  originally  suggested  by 
Professor  Slate. 


49]  THE  EARTH'S  LINES  OF  FORCE.  97 


49.     THE  EAETH'S  LINES  OF  FOECE. 

APPARATUS:    A  sun-dial,  with  compass  attached ;  a  pris- 
matic  compass  ;    a  dipping-needle. 

NOTE.    KEEP  THE  NEEDLES  ARRESTED  so  AS  NOT  TO  WEAR 

OUT  THEIR  POINTS  OF  SUSPENSION  WHEN  NOT  IN  USE. 

I.     Find  the  magnetic  declination  by  either  of  the  two 
following  methods: 

A.  If  the  sun  is  shining,  use  a  SUN-DIAL.  (1.)  Sub- 
tract 9  minutes  from  any  anticipated  reading  of  the  mean 
time  clock(which  gives  the  mean  time  of  the  120th  meridian 
west  of  Greenwich),  to  find  the  local  (Berkeley)  time; 
then  subtract  the  "equation  of  time"  from  the  nautical 
almanac,  or  from  table  44  G,  for  the  given  day  of  the  year, 
to  find  the  "apparent"  or  sun's  time,  which,  owing  to  the 
irregular  motion  of  the  earth,  varies  from  mean  local  time 
by  from  0  to  16  minutes  at  different  times  of  year. 
Example:  Berkeley,  March  8th,  1891,  1.30  P.  M. 

H.  MIN. 

Expected  time  of  observation 2      0 

Subtract  to  reduce  to  local  time  (nearly) +  0      9 

Mean  local  time 1    51 

Subtract  equation  of  time  for  March  8th,  (near ly) .+  0    11 

Apparent  (or  sun's)  time. 1    40 

(2.)  Raise  the  latitude  quadrant  of  the  sun-dial.  — 
Then  raise  the  hour-circle  until  the  arrow  points  to  the 
latitude  (37.8  degrees  for  Berkeley).  Turn  the  shadow-wire 
at  right-angles  to  the  hour-circle,  upward  in  summer,  down- 
ward in  winter  so  as  to  cast  a  shadow  upon  the  hour-circle. 
Set  the  instrument  out  doors  upon  the  nearly  horizontal  sur- 
face of  a  wooden  stool  (glued  not  nailed  together),  and  at  a, 


98  THE  EARTH'S  LINES  OF  FORCE.  [49 

distance  from  any  building  or  structure  containing  iron. 
Turn  the  instrument  until  the  shadow  indicates  approxi- 
mately the  apparent  time.  Level  it  by  means  of  the  foot- 
screws.  When  the  expected  time  arrives,  turn  the  instru- 
ment so  as  to  indicate  exactly  the  corresponding  apparent 
time,  previously  calculated. 

The  fiducial  line  of  the  fixed  circle  of  the  compass  at- 
tached to  the  sun-dial  should  now  indicate  TRUE  north 
and  south.  The  departure  of  the  compass-needle  from 
true  north  is  therefore  to  be  read  from  the  graduated 
circle  of  degrees.  Note  that  this  is  called  the  "magnetic 
declination"  of  the  place. 

B.  If  the  sun  is  not  shining,  use  a  PRISMATIC  COMPASS. 
This  method  requires  the  use  of  two  reference  marks,  the 
second  of  which  has  a  known  bearing  from  the  first.  These 
marks  are  to  be  indicated  by  the  instructor.  Place  the  in- 
strument at  the  first  reference  mark,  and  make  it  as  nearly 
level  as  possible.  Be  sure  that  the  prism  is  uncapped,  and 
that  the  scale  is  in  focus.  Turn  the  instrument  until  the 
second  reference  mark  is  seen  through  the  slit  just  above 
the  prism  so  as  to  be  bisected  by  the  cross-hair.  Lower 
the  eye  until  the  cross-hair  seems  to  intersect  the  scale,  and 
read  the  scale  to  find  the  magnetic  azimuth  of  the  line  join- 
ing the  two  reference  marks.  Subtract  this  from  the  true 
azimuth  of  this  line  (furnished  by  the  instructor)  to  find 
the  magnetic  declination. 

II.  Mount  the  prismatic  compass  upon  a  block  of  wood, 
with  edges  parallel  to  the  line  of  sight,  and  set  it  out  of 
doors  with  the  sides  of  the  block  parallel  to  the  walls  of 
the  building,   but  as  far  away  from  them   as  practicable. 
Find  the  magnetic  azimuth  of  these  walls,  and  deduce  their 
true  azimuth. 

III.  Find  the  magnetic  declination  on  all  the  tables  in 
the  laboratory  by  placing  the  prismatic  compass,  with  the 
edges  of  its  block  parallel  to  the  edges  of  the  tables,  pre- 
viously squared  to  the  walls.      Make  a  map  showing  the 
magnetic  declination  at  the   several  points  examined,  and 


49]  THE  EARTH'S  LINES  OF  FORCE.  99 

draw  contour  lines,  if  possible,  showing  points  of  equal 
magnetic  decimation. 

IY.  Place  the  "dipping-needle  "  on  each  of  the  benches 
where  the  magnetic  declination  has  been  found,  with  the 
plane  of  its  graduated  circle  parallel  to  the  magnetic  meri- 
dian, and  note  the  direction  of  the  earth's  lines  indicated 
by  the  needle.* 

Make  a  map  showing  the  "  dip "  at  several  points,  and 
draw  contour  lines,  if  possible,  connecting  points  of  equal 
dip. 

See  whether  any  similarity  can  be  made  out  between  the 
contour  lines  in  III.  and  IY.,  and  whether  their  similarity, 
if  it  exists,  can  be  attributed  to  the  presence  of  large  masses 
of  iron,  such  as  a  stove,  gas-pipe,  or  a  girder  used  in  the 
construction  of  the  building. 


*  This  method  of  finding  the  "  dip  "  at  different  points  is  sufficiently 
accurate  for  the  purpose  of  drawing  contour  lines.  Accurate  results  with  a 
dipping-needle  require,  in  general,  a  reversal  of  its  bearings  as  well  as  of  its 
magnetism.  The  latter  process  should  not  be  attempted  without  special  in- 
structions. 


100  MAPPING  MAGNETIC  FIELDS.  [50 


50.    MAPPING  MAGNETIC  FIELDS. 

APPARATUS:  A  pair  of  magnets  tested  in  Exp.  46;  some 
iron  filings;  some  blue-print  paper;*  a  sheet  of  common 
paper;  a  small  compass  with  controlling  magnet;  a  sheet  of 
cardboard,  and  some  wax. 

I.  Fasten  one  of  the  magnets  with  wax  to  the  under  side 
of  a  piece  of  blue-print  paper,  a  little  larger  than  the  mag- 
net; mark  in  pencil  upon  the  paper  the  position  of  the  north 
and     south    poles;    scatter     some    iron    filings    over    the 
sensitized   surface,  and   expose   to   the   sunlight   until   the 
paper  turns  blue.      Then  remove  the  magnet  and  the  iron 
filings,  and  wash  the  blue-print  5  or  10  minutes  in  water, 
so  as  to  fix  the  image  of  the  iron  filings. 

II.  Repeat  I.  with  two  magnets  side  by  side,  but  about 
2  cm.  apart,  and  with  similar  poles  opposite. 

III.  Repeat  II.  with  one  of  the  magnets  reversed.     Com- 
pare the  figures  obtained  in  I.,  II.,  and  III. 

IV.  Lay  the  blue-print  obtained  in  I.  on  the  middle  of 
the  sheet  of  ordinary  paper,  and  over  it  the  magnet  used  in 
I.,  with  its  poles  as  nearly  as  possible  in  the  same  relative 
position. 

Place  a  small  compass  at  different  points  of  the  figure, 
and  observe  how  it  points. 

How  does  the  direction  of  the  needle  compare  with  that 
of  the  lines  of  iron  filings  ? 

V.  Neutralize   the    earth's  action  upon  your   compass- 
needle  as  follows:  take  a  sheet  of  cardboard   of  sufficient 
size,  and  square  it  with  the  edges  of  your  table.      Fasten 
your  compass  with  wax  to  the  most  northerly  or  southerly 

*  For  the  preparation  of  blue-print  paper,  see  Exp.  30. 


50]  MAPPING  MAGNETIC  FIELDS.  101 

corner  of  your  cardboard,  as  convenience  may  suggest. 
Kemove  all  magnetic  material  from  the  neighborhood,  and 
draw  in  pencil  a  magnetic  meridian  passing  through  your 
compass.  Neutralize  the  earth's  magnetism  as  in  Exp.  47, 
I.  or  II.,  by  a  controlling  magnet  properly  located.  Be  sure 
to  keep  the  sides  of  the  cardboard  PARALLEL  TO  THE  EDGES 
OF  THE  TABLE  in  the  experiments  which  follow. 

Why  is  your  compass-needle  now  sensitive  to  very  slight 
magnetic  forces? 

VI.  Draw  a  circle,  2  or  3  cm.  in  diameter,  round  each  of 
the  poles,  and  divide   the    circumference   into     10    or  12 
equal  parts.     Through   each   division   draw   a   pencil   line 
parallel  at  every  point  to  the  lines  of  iron  filings  on  each 
side   of  it,  as   far  as  these  lines  can  be  recognized  in  the 
blue-print. 

Place  your  compass-needle,  protected  as  in  V.  from  the 
influence  of  the  earth's  magnetism,  at  the  end  of  one  of 
these  pencil  lines,  and  extend  this  pencil  line  an  inch  or 
more  in  the  direction  indicated  by  the  needle.  Prolong  all 
the  pencil  lines  in  this  way,  an  inch  or  so  at  a  time,  beyond 
the  limits  of  the  blue-print,  as  far  as  the  limits  of  the  sheet 
of  ordinary  paper  beneath  it  will  permit. 

Where  do  the  lines  lead  you  ?  And  what  correspondence 
do  you  observe  between  the  poles  of  the  magnet,  as  located 
in  Exp.  46,  and  the  regions  to  or  from  which  the  lines  of 
magnetic  force  converge  or  diverge  ? 

VII.  With  the  north  and  south  poles,  N  and  S  (located 
in  Exp.  46)  as  centres,  draw   arcs  with  radii  3/4  NS  and 
5/4  NS  respectively,  and  from  their  point  of  intersection, 
I*,  lay  off  a  distance  of  9  cm.  in  the  direction  PS,  to  repre- 
sent the   force  exerted  by  S  upon  a  magnetic  north  pole 
at  P. 

In  what  direction  would  this  same  pole  be  urged  by  N  ? 
and  how  long  a  line  must  be  laid  off  in  this  direction  to 
represent  the  magnitude  of  this  force  (remembering  the 
law  of  inverse  squares  worked  out  in  a  previous  experi- 
ment)? 

Find,  by  the  parallelogram  of  forces,  the  resultant  of  the 


102  MAPPING  MAGNETIC  FIELDS.  [50 

two  forces  on  P.     How  does  this  compare  in  direction  with 
the  lines  of  magnetic  force  in  the  vicinity  of  P?  and  why? 

VIII.  Make  as  in  I.  a  print  showing  the  lines  of  force 
due  to  a  long  thin  coil  of  wire,  carrying  an  electric  current. 
(The  ends  of  the  wire  are  to  be  connected  for  this  purpose 
with  the  poles  of  a  battery.     They  should  remain  connected 
for  as  short  a  time  as  possible,  to  avoid  waste  of  electric 
energy). 

How  do  the  lines  of  force  due  to  the  coil  compare  with 
those  due  to  the  magnet  in  I.  ? 

IX.  Repeat  VIII.  with  a  thin  flat  coil.     What  angular 
relation  exists  between  the  direction  of  the  lines  of  force 
and  the  direction  of  the  wires? 

X.  Make  a  print  showing  the  distribution  of  iron  filings 
due  to  a  current  passing  through  a  vertical  coil  of  wire  in 
the  shape  of  a  hoop,  bisected  by  the  horizontal  plane  on 
which  the  filings  are  spread. 

What  is  the  angular  relation  between  the  lines  of  force 
near  the  wires  and  the  portions  of  wire  nearest  the  iron 
filings? 

What  angular  relation  exists  between  the  lines  of  force 
due  to  the  coil,  and  the  lines  of  force  due  to  a  magnet 
having  its  poles  at  the  points  where  the  coil  cuts  the  hori- 
zontal plane? 


51]  ELECTROMAGNETIC   RELATIONS.  103 


51.    ELECTROMAGNETIC  RELATIONS. 

APPARATUS:  A  jar  of  acid;  a  floating  rectangle  of  wire,  with 
terminals  consisting  of  a  zinc  and  a  copper  plate  dipping  in 
the  acid;  a  permanent  bar  magnet;  a  compass;  and  a  small 
dipping-needle. 

I.  Float  the  rectangle  in  the  jar  of  acid  so  that  the  elec- 
tric current,  which  flows  through  it  (according  to  convention) 
from    the    copper   plate  to   the   zinc  plate,  may  follow   a 
northerly  course  through  the  upper  wire.      Hold  the  corn- 
compass  over  this  wire,  and  as  close  to  it  as  possible.     Is  it 
deflected  at  all?  and  if  so,  toward  the  east  or  the  west? 

II.  Repeat  I.  with  the  compass  under  the  wire. 

III. — IV.     Repeat  I.  and  II.  with  a  southerly  current. 

V.  Find  the  effect  of  an  ascending  current  on  a  compass- 
needle  north  of  it. 

VI.  Repeat  V.  with  the  compass  south  of  the  current. 
VII. — VIII.     Repeat    V.    and    VI.    with    a    descending 

current. 


NOTE.  In  Experiments  IX. — XXIV.,  which  follow,  the 
rectangle  must  be  kept  floating  in  the  middle  of  the  jar,  so 
as  to  be  free  to  move. 

IX.  Hold  the  north  pole  of  your   magnet  over  a  wire 
carrying  a  northerly  current.    In  what  direction  is  it. urged? 

X.  Repeat  IX.  with  the  north  pole  under  the  wire. 
XL — XII.     Repeat  IX. — X.  with  a  southerly  current. 
XIII.     Find  the  effect  of  holding  the  north  pole  of  your 

magnet  close   to   and  on  the  north  side  of  a  wire  of  the 
rectangle  carrying  an  ascending  current. 


104  ELECTROMAGNETIC  RELATIONS.  [51 

XIV.  Repeat  XIII.  with  the  north  pole  on  the  south 
side  of  the  ascending  current. 

XV.— XVI.  Eepeat  XIII.— XIV.  with  a  descending 
current. 

XVII— XXIV.  Eepeat  IX.— XVI.  with  the  south  pole 
of  your  magnet  substituted  for  the  north  pole. 

XXV.     Answer  the  following  questions: 

(1).  How  does  the  reversal  of  the  direction  of  the 
current  affect  your  results  ? 

(2).  How  does  the  substitution  of  a  south  for  a  north 
pole  affect  results? 

(3).  How  does  a  change  of  position  in  a  magnetic  pole 
from  one  side  of  a  wire  to  the  opposite  side  affect  results? 

(4).  How  does  the  direction  in  which  a  magnetic  pole 
(e.  g.  either  pole  of  a  compass-needle)  is  urged  by  a  current 
compare  in  each  case  with  the  direction  in  which  the  wire 
carrying  the  current  is  urged  by  a  similar  pole? 

(5).  What  peculiarity  do  you  observe  in  the  angular  re- 
lation between  the  line  joining  the  (supposed)  agents  in 
these  electromagnetic  phenomena  and  the  direction  of  the 
forces  brought  into  play?  and  what  angle  do  these  two 
directions  make  with  that  of  the  electric  current? 

(6).  Represent  the  direction  of  the  current  in  each  case 
under  I. — VIII. ,  by  the  forefinger  of  your  right  hand. 
Place  your  thumb  ACROSS  your  forefinger,  and  turn  the 
wrist  until  the  thumb  is  above,  below,  north,  south,  east,  or 
west  of  the  finger,  according  to  whether  the  compass  is 
above,  below,  north,  south,  east,  or  west  of  the  current. 
State  in  each  case  whether  the  thumb  does  or  does  not 
represent  the  direction  toward  which  the  north  pole  of  the 
needle  is  deflected. 

XXVI.  Why  do  horizontal  currents  have  no  effect  upon 
a   compass-needle   on  their   own  level  (assuming  that   the 
needle  is  free  to  move  only  in  a  horizontal  plane)? 

Confirm  your  answer  by  the  use  of  a  dipping-needle,  and 
state  how  you  do  this. 

XXVII.  Why  do  easterly  or  westerly  currents  have  in 


51]  ELECTROMAGNETIC  RELATIONS.  105 

general  little  or  no  effect  upon  a  compass-needle  above  or 
below  them? 

Confirm  your  answer  by  the  use  of  a  compass-needle, 
made  to  point  east  and  west  by  means  of  a  controling  mag- 
ent,  as  in  Exp.  47. 

XXVIII.  Why  do  vertical  currents  have  in  general  little 
or  no  effect  upon  a  compass-needle  east  or  west  of  them  ? 
Confirm  your  answer  as  in  XXVII. 

XXIX.  Make  a  diagram  showing  the  path  of  a  magnetic 
pole,  free  to  move  under  the  influence  of  a  vertical  current. 

What  is  the  relation  of  such  a  path  to  the  so-called  lines 
of  force  due  to  the  current?  (Ask  if  you  do  not  know). 

Why  are  the  lines  of  force  in  Exp.  50,  X.,  nearly  circular 
close  to  the  wires? 

XXX.  In  what  direction  should  a  rectangle  (or  coil)  of 
wire  deflect  a  magnetic  needle  at  its  centre  if  the  current  in 
the  upper  side  of  the  rectangle  is  (1)  northward?  (2)  south- 
ward?  (3)  eastward?   (4)  westward? 

How  should  a  (galvanometer)  coil  be  set  up  so  that  the 
magnetic  needle  at  its  centre  may  be  as  sensitive  as  possible 
to  feeble  currents  through  the  coil? 

Confirm  these  conclusions  by  experiment  if  necessary. 

WHEN  YOU  HAVE  FINISHED  WORKING  WITH  THE  FLOATING/ 
APPARATUS,  CLEANSE  IT  WITH  WATER,  AND  SET  IT  TO  DRY. 


106  LAWS  OF  ELECTROMAGNETIC  ATTRACTION.  [52 


52.    LAWS  OF  ELECTEOMAGNETIC  ATTRACTION. 

APPARATUS:  Materials  for  three  rough  tangent-compass 
.galvanometers;  a  battery  and  connecting  wires. 

I.  Take  a  piece  of  insulated  No. -16  wire,  about  4  metres 
long,  and  bend   it  into   a   circular  loop   about  24   cm.  in 
diameter.     Twist  the  free  ends   together,  enough  to   keep 
them  from  separating.     Bind  the  loop  in  a  clamp,  so  that 
its  plane  may  be  vertical,  and  so  that  a  compass  may  be 
placed  at  the  centre  of  the  loop.      Turn  the  clamp  round  so 
that   the   plane   of  the   loop   is   parallel   to   the   magnetic 
meridian,  determined  by  drawing  a  pencil  line  on  the  table 
in  the  direction  indicated  by  the  compass-needle. 

Place  the  compass  at  the  centre  of  the  loop,  and  turn  it 
round  so  as  to  read  zero.  Connect  the  terminals  of  the  loop 
with  a  constant  battery.  (Ask  to  have  the  storage  battery 
connected).  Bead  the  deflection  of  the  compass-needle. 
Then  interchange  the  connections  between  the  battery 
terminals  and  the  terminals  of  the  loop,  and  again  read  the 
deflection.  What  effect  does  this  interchange  have  upon  (1) 
the  magnitude  and  (2)  the  direction  of  the  deflection? 

ALWAYS  REVERSE  YOUR  BATTERY  AND  AVERAGE  THE  TWO 
DEFLECTIONS  TO  FIND  THE  TRUE  DEFLECTION  CAUSED  BY  THE 
CURRENT.  Why  are  errors  in  the  adjustment  of  the  zero 
eliminated  in  this  way  ? 

II.  Eepeat  I.  with  two  turns  of  wire  instead  of  one.  Also 
with  three,  and  also  with  four  turns  of  wire. 

How  does  the  tangent  of  the  angle  of  deflection  compare 
with  the  number  of  turns  of  wire  in  the  coil?  with  the 
length  of  wire  in  the  coil? 

Why  is  the  tangent  of  the  angle  of  deflection  proportional 
to  the  field  of  force  due  to  the  current  ?  (Ask  if  you  do  not 
know). 


52]  LAWS  OF  ELECTROMAGNETIC  ATTRACTION.  107 

III.  Eepeat  I.  with  two  coils  of  wire  having  the  same 
total  length  as  the  single  coil  in  I. 

How  does  the  average  distance  of  the  wire  from  the 
centre  of  the  compass-needle  compare  in  I.  and  III.? 
Assuming  that  the  forces  on  a  magnetic  needle  due  to  a 
current  through  a  given  length  of  wire  are  proportional 
inversely  to  some  integral  power  of  the  mean  distance 
between  the  wire  and  the  needle,  what  is  the  power  in 
question? 

IV.  Set  up  three  instruments  as  in  III.  as  far  apart  as 
may  be  practicable.     Connect  them  with  the  battery  so  that 
the  current  flows  half  through  No.  1,  and  half  through  No. 
2,  but  all  through  No.  3.     Head  the  deflections  of  all  three 
instruments. 

If  the  effect  of  a  current  upon  a  magnet  is  proportional 
to  some  integral  power  of  the  current,  what  is  the  power 
in  question  ? 

Express  the  field  of  force,  F,  at  the  centre  of  a  coil  of 
wire,  as  proportional  directly  or  inversely  to  some  power 
of  the  three  following  quantities  :  (1)  The  current,  C ; 
(2)  the  length  of  wire  in  the  coil,  L  ;  and  (3)  the  radius 
of  the  coil,  E. 


108  TESTING  AN  AMMETER. 


53.     TESTING  AN  AMMETER 

APPARATUS:  A  source  of  electricity;  a  tangent  galvan- 
ometer; a  metre  rod  with  calipers;  an  ammeter,  and  some 
German  silver  wire. 

I.  Set  up  the  ammeter  and  the  tangent  galvanometer  at 
opposite  corners  of  the  table,  so  as  to  free  them  in  so  far  as 
possible  from  mutual  action;  and  adjust  both  instruments 
so  as  to  read  zero.     Pass  a  current  in  series  through  the 
two  instruments.     Twist  the  terminals  of  the  tangent  galva- 
nometer together,  so  that  the  equal  and  opposite  currents 
in  these  terminals  may  neutralize  each  other  in  their  effect 
upon  the  galvanometer.     Do  the  same  with  the  terminals  of 
the  ammeter,  and   with   the  battery  terminals.     Note  that 
the  double  cords,  thus  formed,   resemble  the  letter  T    in 
shape,  the  battery,  galvanometer  and  ammeter  being  situ- 
ated at  the  extremities  of  the  T. 

Make  simultaneous  readings  of  both  ends  of  both  needles, 
(one  in  the  tangent  galvanometer,  the  other  in  the  am- 
meter). 

II.  Kepeat  I.  with  the  terminals  of  the  ammeter  inter- 
changed, so  as  to  reverse  the  current  in  the  ammeter. 

III.  Kepeat  II.  with  the  terminals  of  the  galvanometer 
interchanged,  so   as   to  reverse   the   current  in   the  galva- 
nometer as  well  as  in  the  ammeter. 

IV.  Eepeat  III.  with  the  terminals  of  the  ammeter  as  in 
I.,  so  that  the  current  may  be  reversed  in  the  galvanometer, 
but  not  in  the  ammeter,  as  compared  with  I. 

Note  that  the  arrangements  in  I.. — IV.  represent  every 
possible  combination  of  directions  of  the  current  through 
the  two  instruments. 


53]  TESTING  AN  AMMETER.  109 

Why  is  any  error  in  the  zero  of  either  instrument  elimi- 
nated in  taking  the  average  of  the  four  readings  in  I. — IV.? 

Why  is  the  mutual  action  of  the  two  instruments  elimi- 
nated by  the  same  method?  Would  this  mutual  action  be 
eliminated  by  simply  reversing  the  current  through  both 
instruments? 

V.  Repeat  I. — IV.  with  about  50  cm.  of  No.  25  German 
silver  wire  included  in  the  circuit.     Why  is  the  current  less 
than  before? 

VI.  Repeat  I. — IV.  with    two   coils  of    German    silver 
wire  in  the  circuit. 

VII.  Repeat  I. — IV.  with  the  two  coils  as  in  V.  but  in 
parallel,  not  in  series,  so  that  half  the  current   may  flow 
through  each. 

Under  what  circumstances  do  two  coils  of  wire  diminish 
the  current  from  a  given  source  more,  and  under  what  cir- 
cumstances less,  than  a  single  coil? 

VIII.  Find  the  length  of  wire  in  the  galvanometer  coil; 
also   find   the   mean  radius  of  this  coil.       Given  that  the 
"C.  G.  S."  unit  of  current  is  such  as  to  produce  a  unit  field 
of  force  in  a  coil  of  unit  length  and  unit  radius,  also  that 
the  earth's  field  on  your  table  is  0.24  dynes   per   unit   of 
magnetism,  how  can  you  calculate  the  current  through  the 
tangent  galvanometer  in  I. — IV.?    in  V?    in  VI.?   and   in 
VII? 

Suggestions:  The  strength  of  earth's  field  (0.24)  is  known. 
(Look  up  your  own  determinations  in  Exps.  47  and  48.) 

The  tangent  of  the  angle  of  deflection  gives  the  ratio  be- 
tween the  current's  field,  and  the  earth's  field,  because 
these  are  at  right-angles.  Hence  the  current's  field  can  be 
calculated. 

The  relation  between  the  current  strength,  the  length  of 
wire  in  a  coil,  the  mean  radius  of  the  coil,  and  the 
current's  field  has  been  worked  out  in  the  form  of  a  pro- 
portion in  a  previous  experiment. 

You  are  now  told  to  substitute  equality  for  proportion- 
ality, this  being  the  result  of  the  definition  of  the  C.  G.  S. 
unit  of  current. 


110  TESTING  AN  AMMETER.  [5S 

In  the  equation  thus  obtained,  all  the  quantities  are 
known  except  the  current,  hence  the  current  can  be 
calculated. 

IX.  Given  that  the  units  indicated  by  the  ammeter  are 
some  decimal  multiple  or  submultiple  of  C.  G.  S.  units,, 
what  is  the  multiple  or  submultiple  in  question? 


54]  HEAT  AND  RESISTANCE.  Ill 


54.    HEAT  AND  KESISTANCE. 

APPARATUS  :  A  source  of  electricity,  two  coils  of  No.  25 
German  silver  wire,  about  50  cm.  each;  an  ammeter;  a 
calorimeter,  and  a  thermometer ;  access  to  a  clock,  and  to 
scales  with  weights. 

NOTE.  The  electrical  resistance  of  a  conductor  depends 
upon  the  power  necessary  to  maintain  a  given  current 
through  it.  The  power  is  invariably  transformed  into  heat, 
and  the  object  of  this  experiment  is  to  measure  it  by  means 
of  its  heat  equivalent.  The  unit  of  power  adopted  in 
practical  use  is  the  "watt,"  or  10,000,000  dynes  with  a 
working  velocity  of  1  cm.  per  sec.  The  relation  between 
the  heat  unit  and  the  watt  can  be  made  out  from  your  own 
observations  as  follows : 
1  unit  of  heat  per  sec.  —  about  30  gram-degrees  of  lead 

shot  per  sec.  (Exp.  19). 
1  gram -degree  of  lead  shot  per  see.  =  about  1420  gram-cm. 

of  work  per  sec.  (Exp.  21). 
1  gram-cm,  of  work  per  sec.  =  about  980  dyne-cm,  of  work 

per  sec.  (Exp.  45). 

1  dyne-cm,  of  work  per  sec.  =  .000,000, 1  watt  (by  definition). 
Therefore  1  unit  of  heat  per  sec.  =  about 

30  X  1420  X  980  X  .000,000,1  =  4.17  watts. 

I.  Weigh  the  inner  cup  of  the  calorimeter,  and  place  in 
it  about  50  grams  of  water,  at  a  temperature  some  5  degrees 
below  that  of  the  room;  pass  an  electric  current  in  series 
through  the  ammeter  (previously  adjusted  so  as  to  read 
zero)  and  through  one  of  the  coils  of  German  silver  wire. 
Immerse  this  coil  in  the  water  of  the  calorimeter.  Note 
the  temperature  every  minute  for  about  10  minutes,  stirring 
continuously  between  observations.  Note  also  the  corre- 
sponding readings  of  the  ammeter. 


112  HEAT  AND  RESISTANCE.  [54 

What  is  the  effect  of  passing  a  current  through  the  con- 
ductor upon  the  temperature  of  this  conductor  and  the 
water  in  contact  with  it? 

II.  Eepeat  I.  with  the  second  coil  of  wire  also  included 
in  the  circuit,  but  not  immersed  in  the  calorimeter. 

What  is  the  effect  of  interposing  this  additional  length  of 
•wire  (1)  upon  the  magnitude  of  the  current?  and  (2)  upon 
the  amount  of  heat  generated  in  a  given  time  ? 

Assuming  that  the  amount  of  heat  generated  in  a  given 
conductor  in  a  given  time  is  proportional  to  some  integral 
power  of  the  current  as  measured  by  the  ammeter,  what  is 
-the  power  in  question? 

III.  Eepeat  II.  with  both  coils  immersed  in  the  water. 
How  does  the  heating  of  a  conductor  by  a  given  current 
compare  with  the  length  of  wire  traversed  by  that  current? 

IV.  Repeat  III.  with  the  two  coils  arranged  so  that  half 
of  the  current  traverses  each. 

What  is  the  effect  upon  the  magnitude  of  the  current, 
due  to  paralleling  a  conductor  with  another  conductor  ? — 
(Compare  Exp.  53,  VII) 

V.  Calculate  in  each  case  (I. — IV.)  the  water  equivalent 
of  the  calorimeter  and  its  contents  (by  adding  2  grams  to 
the  weight  of  water  which  it  contains),  then  the  No.  of  heat 
units   (gram-degrees)   developed  in  one   second,   then   the 
equivalent  power  in  watts  (see  introductory  note).       Divide 
the  power  in  watts  by  that  power  of  the  current  to  which 
you  judge  the  heating  effects  to  be  proportional.     Note  that 
this  quotient  is  called  the  resistance  of  the   conductor  in 
question,  and  that  it  is  given  in  "ohms." 

How  does  the  resistance  in  ohms  of  a  given  conductor 
compare  in  I.  and  II.?  How  does  the  resistance  of  a  given 
conductor  compare  with  that  of  two  similar  conductors  in 
series?  in  parallel? 


55]  DIVIDED  CIRCUITS.  113 


55.    DIVIDED  CIRCUITS. 

APPARATUS:    A    constant    battery,    an    ammeter,    a    mi- 
crometer, and  a  rheostat. 

I.  Find   the   diameter    of    the    rheostat    wires   with   a 
micrometer.     Pass   the  current  from  the   battery   through 
the  ammeter,  then  through  80  cm.  of  the  large  wire  of  the 
rheostat.        This  is  done  by  means  of  a  sliding  clamp,  fixed 
at  80  cm.  from  one  of  the  binding  screws.      Note  the  deflec- 
tion of  the  ammeter. 

II.  Substitute  for  80  cm.  of  the  large  wire,  such  a  length 
of  the  first  small  wire  as  may  be  necessary  to  reduce  the 
deflection  of  the  ammeter  to  the  same  amount   as  before. 
Note  the  length  of  the  wire  in  question. 

III.  Pass    the    current    through    two    small    wires    in 
parallel,   making  the  lengths   equal,  and  find  what  length 
will  give  the  same  current  as  before. 

IV.  Repeat  III.  with  three  small  wires  in  parallel. 

V.  Repeat  III.  with  four  small  wires  in  parallel. 

VI.  Repeat  V.  with  the  same  lengths  of  wire  in  series 
instead    of    in    parallel,   and    note    the   deflection  of  the 
ammeter. 

VII.  Pass  the  current  through   the  ammeter   and  then 
through  the  whole  length  of  the  large  wire  with  one  of  the 
small  wires   in  parallel,   and    note  the   deflection  of   the 
ammeter. 

VIII.  With  the  connections  as  in  VII.,  in  other  respects, 
take  the  ammeter  out  of  the  main  circuit,  and  insert  it  in 
the  branch  circuit  containing  the  larger  wire  of  the  rheostat. 

IX.  Transfer  the  ammeter  to  the  branch  circuit  contain- 
ing the  smaller  wire  of  the  rheostat. 

X.  Answer  the  following  questions: 

8 


114  DIVIDED    CIRCUITS.  [55 

1.  How  do  the  resistances  of  the  rheostat  in  I.,  II.,  III., 
IV.,  and  V  compare  and  why?     (Ask  if  you  do  not  know). 

2.  Does  a  large  or  a  small  wire  of  given  length  offer  the 
greater  resistance  to  an  electric  current  ?     (Assume  that  the 
resistance   of   a  wire  is   proportional  to   its  length,   other 
things  being   equal,  and   that,  consequently,  if  a  smaller 
length   of  one   wire   is   equivalent   to  a  greater  length  of 
another,    the     former    has    the    greater    resistance    for  a 
given  length. 

3.  How  does  the  resistance  of  a  given  length  of  a  double, 
treble,  or  quadruple  wire  of  a  given  sort  compare  with  that 
of  a  single  wire  ? 

4  How  does  the  resistance  of  a  given  length  of  a  large 
wire  compare  with  that  of  an  equal  length  of  several  small 
wires  of  the  same  material,  in  parallel,  when  the  total  cross- 
section  of  the  small  wires  is  equal  to  that  of  the  large  wire? 
(Bear  in  mind  that  the  cross-section  varies  as  the  square  of 
the  diameter). 

5.  If  the  resistances  of  equal  lengths  of  a  wire  of  given 
material  are  proportional  to   some  integral  power   of  the 
cross-section   (directly  or  inversely),   what  is  the   propor- 
tionality in  question? 

6.  Is  the  resistance  of  several  wires  in  parallel  the  same 
as  in  series?        What  evidence  have  you  on  this  point  from 
this  experiment? 

7.  Is    the    resistance    of    a    large     wire    increased    or 
diminished  by  the  addition  ,  of  a  small  wire   of  the   same 
length  in  parallel  ? 

8.  Does  the  greater  portion  of  the  current  in  a  divided 
circuit  flow  through  the  channel  of  greater  or  less  resistance 
in  your  experiments  ? 

9.  Assuming  that  the  portions  of  a  current  in  a  divided 
circuit  are  proportional  to  some  power,  direct  or  inverse,  of 
the  resistances  of  their  respective  channels,  what  is  the  pro- 
portion in  question? 


56]  ELECTRICAL   EFFICIENCY.  115 


56.    ELECTEICAL  EFFICIENCY. 

APPARATUS :  Two  beakers  of  about  100  grams  capacity ;  a 
small  zinc-carbon  pair  to  fit  into  either  beaker;  a  resistance- 
coil  (about  1  ohm,  acid  proof) ;  some  bichromate  battery 
solution ;  a  thermometer ;  a  balance  with  weights  to  1  deci- 
gram, and  access  to  a  minute  clock. 

I.  Make   a    mark  on  both  beakers  corresponding  to   a 
capacity  of  100  cu.  cm.;  weigh  the  zinc-carbon  pair,  place  it 
in  one  of  the  beakers,  and  fill  this  beaker  with  bichromate 
solution  until  it  comes  up  to  the  100  cu.  cm.  mark  WITH  THE 

BATTERY  IN  PLACE. 

Connect  the  two  terminals  of  the  resistance-coil  with  the 
screw-cups  of  the  battery,  and  immerse  the  coil  in  the  bi- 
chromate solution  beside  the  plates  of  the  battery.  Note 
the  temperature  every  minute  until  it  has  risen  10  degrees, 
stirring  the  liquid  all  the  time  by  moving  the  plates  of  the 
battery.  Eeweigh  the  zinc-carbon  pair. 

II.  Eepeat  the  experiment  with  the  zinc-carbon  pair  in 
the   second  beaker,  filled  up  to  the  100  cu.  cm.    mark   as 
before;    but  place  the  resistance  coil  in  the  first  beaker, 
containing  the   exhausted  battery   solution,   cooled  to   its 
original  temperature  by  ice,  or  otherwise,  and   filled  up  so 
as  to  occupy  100  cu.  cm.  as  before.     In  the  repetition  of  this 
experiment,  note  every  minute -the  temperature  not  only  of 
the  battery,  but  also  that    of  the    beaker  containing  the 
resistance-coil,  and  stop  the  experiment  when  the  current 
has  run  about  the  same  time  as  in  I. 

NOTE.  The  object  of  having  100  cu.  cm.  always  in  the 
beakers  is  that  the  thermal  capacity  may  be  as  nearly  as 
possible  the  same.  The  thermal  capacity  of  the  zinc-carbon 


116  ELECTSICAL  EFFICIENCY.  [56 

pair  is  not  very  far  from  that  of  an  EQUAL  BULK  of  battery 
solution. 
Answer  the  following  questions : 

1.  Calling  the  thermal  capacity  of  each  beaker  with  its 
contents  100  units,  find  the  No.  of  heat  units  developed  by 
the  battery  in  I. 

2.  Assuming  that  the  carbon  pole  of  the  battery  is  un- 
acted upon,  how  much  zinc  has  gone  into  solution? 

3.  If  the   heat  developed  is  due  to  the  solution  of  the 
zinc,   how  many  units   of  heat  would  one   gram   of  zinc 
account  for? 

4.  Find   the  number  of  heat  units  developed  by  the 
solution  of  one  gram  of  zinc  (a)  in  the  battery  in  II.  and  (b) 
in  the  beaker  containing  the  resistance-coil  in  II.      Why  is 
the  result  in  4  (a)  less  than  in   3  ? 

5.  How  does  the  total  number  of  heat  units  developed 
by  one  gram  of  zinc  in  II.    compare   with  that  in  I.?  and 
why? 

6.  Find  the  proportion  of  chemical  energy  of  the  battery 
transmitted  to  the  resistance-coil.     What  name  is  given  to 
such  a  proportion?     (Ask  if  you  do  not  know.) 


57]  ELECTROCHEMICAL  RELATIONS.  117 


57.    ELECTEOCHEMICAL  KELATIONS. 

APPARATUS:  Two  Daniell  cells,  three  vessels  filled  with 
sulphate  of  copper  solution,  six  copper  plates,  and  an 
ammeter.  Access  to  scales  with  weights  to  1  decigram.  A 
jar  of  water. 

I.  Weigh  each  of  the  six  copper  plates,  also  the  two 
copper  poles  of  the  Daniell  cells.  In  each  of  the  vessels 
containing  sulphate  of  copper,  immerse  a  pair  of  copper 
plates,  so  that  a  current  cannot  pass  from  one  of  a  given 
pair  to  the  other  without  traversing  the  liquid.  Note  that 
the  three  instruments  thus  formed  are  called  copper 
voltameters. 

Connect  the  Daniell  cells  in  series,  and  let  the  current 
pass  in  series  through  the  ammeter  and  through  one  of  the 
copper  voltameters.  Then  let  the  current  divide  so  that 
one  part  passes  through  the  second  voltameter  and  the 
other  part  through  the  third  voltameter.  The  whole 
current,  uniting  again,  must  return  to  the  battery. 

Let  the  current  run  for  50.8  minutes.  Note  the  deflection 
of  the  ammeter  every  minute  during  this  time.  Then  wash, 
dry  and  reweigh  the  six  copper  plates  and  the  poles  of  the 
Daniell  cells. 

Answer  the  following  questions: 

(1)  Have  the  poles  of  the  Daniell  cells  gained  or  lost  in 
weight?  and  by  an  equal  or  by  an  unequal  amount? 

(2)  Which   of  the   voltameter   plates  have  gained,  and 
which  have  lost  in  weight?     State  whether  the  current  from 
the  copper  pole  of  the  Daniell  battery  entered  the  liquid  by 
the  plate  or  left  liquid  by  the  plate  in  each  case. 

(3)  Is  copper  carried  with  or  against  the  current? 


118  ELECTROCHEMICAL    RELATIONS.  [57 

(4)  How  do  the  changes  of  weight  of  two   plates  of  a 
given  voltameter  compare  in  sign  and  in  magnitude  ? 

(5)  How  does  the  change  in  weight  of  the  poles  of  the 
Daniell  cells  compare  with   that   of  the  voltameter  plates 
transmitting  the  whole  current? 

(6)  How  do  the  changes  of  weight  in  the  plates   of  a 
voltameter  transmitting  the   whole  current  compare  with 
those  of  the  voltameters  transmitting  each  a  fraction  of  the 
current  ? 

(7)  If  the  amount  of  copper  deposited  on  one   of   the 
plates   of  a  voltameter   is   proportional   to  some   integral 
power  of  the  current,  what  is  the  power  in  question? 

(8)  How  does   the   weight  of   copper  deposited  by   a 
current    in    50.8   minutes   compare    with    the    current    in 
amperes,  as  indicated  by  the  ammeter? 


58]  ARRANGEMENT  OF  BATTERIES.  119 


58.    AKEANGEMENT  OF  BATTEEIES. 

APPARATUS  :     Two  Daniell  cells ;  1  Bunsen  cell ;  an  am- 
meter ;  a  resistance-coil,  and  connecting  wires. 

I.  Connect  one  of  the  Daniell   cells  with  the  ammeter 
and  resistance-coil  in  parallel.     Note  the  deflection. 

Disconnect  the  terminals  of  the  resistance-coll  so  that  the 
whole  current  flows  through  the  ammeter.  Is  the  reading 
of  the  ammeter  greatly  affected  by  this  change?  How  do 
you  explain  this  fact  ? 

II.  Connect  the  resistance-coil    and  ammeter  with  the 
Daniell  cell  in  series,  and  note  the  deflection;  then  shunt 
out  the  resistance-coil  with  a  short,  thick  copper  wire.     Is 
the  reading  of  the  ammeter  greatly  affected?  and  why? 

From  your  results  in  I.  and  II.  give  some  idea  of  the 
relative  resistances  of  the  ammeter  and  the  resistance-coil, 
the  ammeter  and  the  battery,  also  the  resistance-coil  and 
the  battery,  assuming  that  the  resistances  are,  other  things 
being  equal,  inversely  as  the  currents  which  traverse  them. 

III.  Find   the  reading  of  the  ammeter   when   connected 
with 

(a)  a  single  Daniell  cell. 

(b)  the  other  Daniell  cell, 

(c)  the  two  Daniell  cells  in  series, 

(d)  the  two  Daniell  cells  in  parallel, 

(e)  the  Bunsen  cell, 

(f )  the  Bunsen  cell  and  the  two  Daniell  cells  in  series. 
How  should  cells  be  connected  (in  series  or  in  parallel) 

to  give  a  maximum  current  through  a  galvanometer  of  low 
resistance? 


120  ARRANGEMENT  OF  BATTERIES.  [58 

IV.  Kepeat  III.  (a) — (f)  with  the  resistance-coil  in  series 
with  the  ammeter. 

How  should  cells  be  connected  so  as  to  give  a  maximum 
current  through  a  high  resistance? 

Would  you  prefer  a  galvanometer  of  high  or  low  resis- 
tance to  appreciate  effects  due  to  combining  cells  in  parallel? 

Should  the  resistance  of  a  galvanometer  be  high  or  low 
if  the  instrument  is  to  be  used  in  estimating  effects  due  to 
combining  cells  in  series. 

Note  that  such  a  galvanometer  is  called  a  voltmeter. 


59]  ELECTROMOTIVE  FORCE.  121 


59.    ELECTROMOTIVE  FORCE. 

APPARATUS:    A  Bunsen  cell,  3  Daniell  cells,  two  Leclanche 
cells,  and  a  voltmeter. 

I.  Connect  the  voltmeter  with  two  of  the  Daniell  cells 
in  series,  but  joined  copper  to  copper,  (or  zinc  to  zinc)  so 
that  their  "electromotive  forces"  are  opposed  to  each  other. 
Are  the  two  electromotive  forces  unequal  or  (nearly)  equal? 
Give  reasons  for  your  answer. 

II.  Repeat  I.  with  a  different  pair  of  Daniell  cells. 

III.  Repeat  I.   with  the  third  possible  pair  of  Daniell 
cells.     What  reason  have  you  for  thinking  that  all  three 
cells  are  approximately  equal  in  electromotive  force? 

IV.  Repeat  I.  with  two  cells  in  series  connected  copper 
to  zinc,  so  that  their  electromotive  forces  may  act  in  the 
same  direction. 

V.  Repeat   IV.   with  the  three  Daniell  cells  in   series, 
connected  copper  to  zinc  in  each  case. 

How  does  the  readings  of  the  voltmeter  compare  with  the 
joint  electromotive  force  in  the  circuit  in  I. — V.  ? 

VI.  Repeat  V.  with  one  of  the  cells  reversed,  so  as  to 
act  in  opposition  to  the  other  two. 

What  is  the  effective  electromotive  force  in  this  case,  and 
how  does  it  compare  with  the  reading  of  the  voltmeter? 

VII.  Assuming   now   that  the   voltmeter   will   measure 
correctly   the  electromotive  force  in  every  case,   find   the 
electromotive  force  of  each  Leclanche  cell,  and  of  two  Le- 
clanche cells  in  series,  also  the  electromotive  force  of  the 
Bunsen  cell. 

VIII.  Oppose  the  Bunsen  cell  in  series  against  as  many 
Daniell  cells  as  should  give  about  the  same  electromotive 
force,  and  find  the  effect  of  the  combination  on  the  voltmeter. 


122  ELECTROMOTIVE  FORCE.  [59 

IX.  Oppose  as  many  Leclanche  cells  as  may  be  equal  in 
electromotive   force   to   a  given   number   of   Daniell   cells 
against  the  number  of  Daniell  cells  in  question,  and  find 
*the  effect  upon  the  voltmeter. 

What   in  general  do  you   conclude   to  be   the  effect  of 
opposing  batteries  with  equal  electromotive  forces  ? 

X.  Join  two  Daniell  cells  in  parallel,  and  oppose  them 
to  a  single  cell  in  series  with  the  voltmeter. 

How  does  the  electromotive  force  of  two  cells  in  parallel 
compare  with  that  of  a  single  cell  of  the  same  kind? 

XI.  Test  your  conclusion  in  X.  by  actual  measurement 
with  the  voltmeter,  upon  one,  two,  and  three  Daniell  cells 
in  parallel. 

What  in  general  is  the  effect  of  joining  cells  (of  a  given 
kind)  in  parallel  upon  their  joint  electromotive  force? 

XII.  Find  the  electromotive  force  of  three  Daniell  cells 
in  series  with  the  two  Leclanche  cells  and  the  Bunsen  cell. 

What  in  general  is  the  effect   of  joining  cells  in  series 
:upon  their  joint  electromotive  force  ? 


60]  OHM'S  LAW.  123 


60.    OHM'S   LAW. 

APPARATUS:  Two  Daniell  cells;  1  Bunsen  cell;  an 
ammeter;  a  voltmeter;  a  rheostat. 

I.  Measure  off  lengths  of  German  silver  wire,  the  same 
size  as  that  used  in  Exp.  54,  sufficient  to  give  resistances  of 
1,  2,  5,  and  10  ohms.      (Consult  results  of  Exps.  54,  and  55). 

Send  a  current  from  1  Daniell  cell  through  each  of  the 
resistances  in  turn,  and  note  the  deflection,  in  each  case,  of 
an  ammeter  included  in  the  circuit,  in  series  with  the 
resistance  in  question.  Also  note  the  indication  of  a 
voltmeter  connecting  the  poles  of  the  cell. 

II.  Kepeat  I.  with  two  Daniell  cells  in  series. 

III.  Bepeat  I.  with  two  Daniell  cells  in  parallel. 

IY.  Repeat  I.  with  the  Bunsen  cell  instead  of  the 
Daniell. 

V.  Repeat  I.  with  the  Bunsen  and  two  Daniell  cells  in 
series. 

VI.  Make    a  table   showing   in   the   first    column,   the 
currents  in  amperes,  in  the  second  column,  the  resistances 
in  ohms  corresponding  to  these  currents,  and  in  the  third 
column,    the    corresponding    readings    of    the    voltmeter. 
Calculate  a  fourth  column  showing  the  product  in  each  case 
of  the  current  and  resistance. 

How  do  the  products  of  current  and  resistance  compare 
with  the  indications  of  the  voltmeter? 

Given  that  the  product  of  the  resistance  of  a  conductor  in 
ohms  and  the  current  in  amperes  which  traverses  it  is 
equal  to  the  difference  of  potential  or  "electromotive  force" 
in  volts  between  its  terminals,  what  is  the  value  in  volts  of 
the  divisions  of  the  voltmeter?  (Assume  that  these 

divisions  represent  some  simple  multiple  or  submultiple  of 
a  volt). 


124  OHM'S  LAW.  [60 

Find  a  simple  law  expressing  the  current  in  terms  of 
resistance  and  electromotive  force  (OHM'S  LAW). 

VII.  Find  as  in  Exp.  59  the  electromotive  force  of  each 
combination  of  cells  mentioned  in  I. — V.,  also  find,  as  in 
Exp.  58,  the  current  sent  by  each  through  the  ammeter  with 
connecting  wire  of  practically  no  resistance.  Calculate  by 
Ohm's  law  the  resistance  of  each  combination  of  cells. 

How  does  the  resistance  of  a  battery  consisting  of  two 
cells  in  parallel  compare  with  that  of  a  single  cell  ? 

How  does  the  resistance  of  two  cells  in  series  compare 
with  that  of  a  single  cell  ? 

Calculate  by  Ohm's  law  the  electromotive  force  of  the 
cells  in  I.  and  II.,  remembering  to  add  the  battery 
resistance  to  that  of  the  rheostat.  Is  this  electromotive 
force  constant? 


61]       FALL  OF  POTENTIAL  ALONG  A  CONDUCTOR.       125 


61.    FALL  OF  POTENTIAL  ALONG  A  CONDUCTOR 

APPARATUS:  Two  or  more  batteries;  an  ammeter;  a 
voltmeter;  and  a  rheostat. 

I.  Pass  a  current  in  series  through  the  ammeter  and  the 
rheostat.          Find    by    the   voltmeter    the    difference    of 
potential  at  the  extremities  of  one  of   the   rheostat   wires 
having  a  resistance  of  one  ohm. 

Repeat  with  different  wires  having  also  resistances  of  one 
ohm. 

How  do  the  readings  of  the  voltmeter  compare  with  one 
another. 

How  do  the  readings  of  the  voltmeter  compare  with 
those  of  the  ammeter  and  why? 

II.  Connect  one  terminal  of  the  voltmeter  with  one  of 
the  battery  poles,  and  connect  the  other  end  with  different 
points  on  the  rheostat.      Note  the  reading  of  the   voltmeter 
in  each  case. 

How  do  the  readings  of  the  voltmeter  compare  with  the 
resistances  in  the  main  circuit  between  the  points  of 
contact  ? 

III.  Eepeat  II.  with  the  fixed  terminal  of  the  voltmeter 
connected  with  the  other  pole  of  the  battery. 

IV.  Eepeat  II.  or  III.  with  a  stronger  battery. 

How  does  the  fall  of  potential  between  two  points  com- 
pare with  the  current? 

V.  Make   as  in   Exp.  60  a   table   showing  the  relation 
between  the  readings  of  the  voltmeter  and  the  products  of 
the  current  and  resistance  between  its  poles. 

Does  Ohm's  law  apply  to  portions  of  a  circuit  as  well  as 
to  the  circuit  as  a  whole? 


126      FALL  OF  POTENTIAL  ALONG  A  CONDUCTOR.       [61 

VI.  Pass     a    current    through    the    ammeter    and     an 
unknown  resistance   in   series.        Find  the   difference   of 
potential    between  the   two   terminals    of    this    unknown 
resistance. 

Calculate  the  resistance  in  question  by  principles  already 
worked  out. 

VII.  Draw   one   or   more   curves   showing  the    fall   of 
potential  between  the   two  poles  of  a  battery.       Lay   off 
resistances   as   abscissas,   and   differences   of  potential   as 
ordinates.         Mark  each  curve  with  a  number  representing 
the  current  in  amperes. 


62]  ELECTBICAL  POWER.  12.7 


62.    ELECTEICAL  POWER 

APPARATUS :  A  source  of  electricity;  an  electric  motor;  a 
transmission  dynamometer,  and  a  friction  brake.  A  volt- 
meter and  an  ammeter. 

I.  Send  a  current  through  the  motor  and  through  the 
ammeter  in  series.  Connect  the  terminals  of  the  motor 
through  the  voltmeter  as  a  shunt.  Read  both  instruments. 
Multiply  the  current  in  amperes  by  the  electromotive  force 
in  volts  to  find  the  electrical  power  in  watts  spent  upon  the 
motor.  (Ask  why  if  you  do  not  know). 

Find  the  tension  in  dynes  (1  gram  weight  equals  980 
dynes  at  Berkeley)  on  each  cord  of  the  transmission 
dynamometer,  remembering  that  twice  this  tension  is  felt 
by  the  spring  balances,  and  find  by  subtraction  the 
difference  in  tension  between  the  two  cords  leading  to  and 
from  the  pulley  of  the  motor.  Find  the  total  length  of  the 
cord,  and  the  time  of  one  complete  journey  around  the 
pulleys,  by  means  of  the  appropriate  observations.  Calcu- 
late the  velocity  of  the  cord  in  centimetres  per  second. 

Find  the  power  in  watts  transmitted  through  the 
dynamometer  by  multiplying  together  the  velocity  of  the 
cord  in  centimetres  per  second  and  the  difference  of  tension 
in  dynes,  and  pointing  off  seven  places  of  decimals.  (See 
Exp.  54,  introductory  note.) 

Find  the  ratio  of  the  power  utilized  (through  the  trans- 
mission dynamometer)  to  the  power  spent  by  the  source  of 
electricity  on  the  motor.  What  name  is  given  to  this  ratio? 
(Ask  if  you  do  not  know). 


128  ELECTRICAL  POWER.  [62 

II.  Eepeat  I.  with  different  amounts  of  friction  upon 
the  machinery  set  in  motion  through  the  transmission 
dynamometer.  Find  (1)  the  maximum  power  of  the  motor 
with  the  given  source  of  electricity,  and  (2)  the  maximum 
efficiency  of  the  motor  under  the  conditions  of  the 
experiment. 


63]  MAGNETIC-ELECTRIC   INDUCTION.  129 


63.    MAGNETO-ELECTRIC  INDUCTION. 

APPARATUS:  A  ballistic  galvanometer;  2  coils  of  wire, 
with  magnetized  steel  and  soft  iron  cores;  a  wire  to  shunt 
the  galvanometer,  and  a  battery. 

I.  Make  sure  that  your  galvanometer  is  free  to  swing, 
and  find  (1)  which  of  the  rods  is  the  steel  magnet,  and  (2) 
which  end  of  thisvrod  is  the  north  pole,  by  its  action  on  the 
galvanometer  needle. 

Connect  the  two  terminals  of  the  galvanometer  with  the 
shunt  provided  for  this  purpose,  so  that  it  will  not  be  too 
sensitive,  and  find,  by  connecting  the  galvanometer  with  the 
battery,  which  terminal  of  the  galvanometer  should  be 
joined  to  the  positive  (carbon  or  copper)  pole  in  order  that 
the  deflection  may  be  right-handed. 

Remove  the  shunt  and  see  that  the  galvanometer  is  once 
more  in  working  order.  Connect  it  with  the  terminals  of 
the  smaller  coil.  Insert  the  north  pole  of  the  magnet  into 
this  coil,  and  note  the  behavior  of  the  galvanometer.  If  it 
moves  at  all,  state  whether  the  motion  is  sudden,  or 
gradual,  and  whether  the  deflection  is  permanent  or 
temporary. 

II.  When  the  galvanometer  needle^  has   come   to   rest, 
suddenly  withdraw  the  magnet.      Note  the  deflection  of  the 
galvanometer. 

Is  the  direction  of  the  deflection  the  same  in  II.  as  in  I.  ? 
In  what  direction  does  the  induced  current  circulate  in  the 
coil,  as  seen  from  a  point  outside,  looking  toward  the  north 
pole,  in  I.  and  in  II.  ? 

III.  Eepeat  I.  and  II.  with  the  south  pole  for  the  north 
pole. 

IV.  Repeat  I.  with  the  soft  iron  instead  of  the  steel. 


130  MAGNETIC-ELECTRIC    INDUCTION.  [63 

V.  With   the   soft   iron  still  within   the   coil,  find  the 
effect  of  touching  one  end  of  the  soft  iron  with  the  magnet. 
How  does  this  compare  with  the  effect  of  introducing  the 
same  pole  within  the  same  opening  of  the  coil? 

VI.  Find   as   in   V.    the   effect   of  breaking  connection 
between  the  soft  iron  and  the  magnet. 

VII.  Place   the    magnet   within  the   coil,  and  find   the 
effect  of  touching  the  soft  iron  to  one  end  of  it.     Can  this 
be  accounted  for  by  supposing  the  magnetic  pole  to  spread 
along  the  iron? 

VIII.  Find  the  effect  of  breaking   connection  between 
the  magnet  and  the  iron,  and  compare  the  result  with  that 
in  VII. 

IX.  Connect  the  larger  coil  with  the  galvanometer,  place 
the  smaller  coil  within  it,  and  find  the  effect  of  connecting 
the  terminals  of  the  smaller  coil  (when  within  the  larger 
coil)  with  the  battery.      Is  the  induced  current  in  the  same 
direction  as  that  of  the  inner  coil  ? 

X.  Find  as  in  IX.  the  effect  of  breaking   the   primary 
current,  and  compare  results  in  IX.  and  X. 

XI.  Find  the  effect  of  introducing  and  the  effect  of  with- 
drawing  the   primary   coil   while   the   current  is    flowing 
through  it,  and  compare  results  with  those  due  to  making 
and  breaking  the  current  in  the  coil  without  removing  it. 

XII.  Repeat  X.  with  a  soft  iron  core  in  the  inner  coil. 
How  are  the  effects  modified  by  the  core  (1)  in  sign  and  (2) 
in  magnitude? 


64]  EARTH-INDUCTOR.  131 


64    EAKTH-INDUCTOK. 

APPARATUS:  A  Delezenne's  circle;  a  ballistic  galva- 
nometer. 

I.  Set   the   Delezenne's   circle   at   one   corner   of  your 
table,  and  the  ballistic  galvanometer  at  the  opposite  corner. 
Turn  the  base  of  the  circle  so  that  the  brass  plate,  gradu- 
ated to  5  degrees,  may  lie   in   a  vertical  north  and  south 
plane.       Make  the  axis  of  revolution  horizontal.       Connect 
the  terminals  of  the  circle  with  the  galvanometer.     Make 
sure   that  the   galvanometer   is   free  to  move.      (It  is   so, 
probably,  if  it  responds  to  the  approach  of  your  knife,  or 
other  steel  object). 

Turn  the  coil  slowly  into  a  horizontal  position.  Then 
turn  it  suddenly  into  a  vertical  plane.  Note  the  action  of 
the  galvanometer.  How  do  you  account  for  this  ? 

II.  Turn  the  coil  suddenly  into  a  horizontal  position, 
continuing  the  direction  of  rotation  in  I.      Compare  effects, 
and  explain  the  result. 

III.  Turn  the  coil  in  the  same  direction  of  rotation  as  in 
I.  and   II.,  through   another   right-angle.      How   does   the 
effect  upon  the  galvanometer  in  III.  compare  with  that  in 
I.  and  why?      (Examine  carefully  the  construction  of  the 
"commutator"  on  the  axis  of  rotation  before  answering  this 
question). 

IV.  Turn  the   coil  still  farther,  back  into    its   original 
position,  and  note  the  effect. 

V.  Find  the  effect    of    continuous    rotation  of  the  coil 
to  the  right.     What  would  this  effect  be  if  there  were  no 
commutator  ? 

VI.  Find  the  effect  of  reversing  the  direction  of  rotation 
of  the  coil. 


132  EARTH-INDUCTOR.  [64 

VIL  Set  the  circle  so  as  to  revolve  about  a  vertical  axis, 
with  the  brass  graduated  plate  (as  in  I.  and  VI.)  in  a  north 
and  south  plane.  Find  the  effect  of  continuous  rotation  as 
before. 

VIII.  Turn  the  base  of  the  instrument  through  a  right- 
angle,  and  again  find  the  effect  of  continuous  rotation. 

Explain  if  you  can  the  effect  of  turning  the  base  of  the 
instrument  through  90  °  .  (If  you  cannot,  ask  for  help). 

IX.  Assuming  that  the  effects  (as  measured  by  the  galva- 
nometer) in  V.  and  in  VII.   are  to  each  other  as  the  vertical 
and  horizontal  components  of  the  earth's  magnetism,  what 
is  the  tangent  of  the  dip  ?  and  what  (see  table  of  tangents) 
is  the  dip  of  the  earth's  magnetism  ? 

Turn  the  base  of  the  instrument  back  to  its  original 
position  in  I. — VI.,  and  clamp  the  circle  by  a  series  of  trials 
at  such  an  angle  that  continuous  rotation  fails  to  affect  the 
galvanometer.  What  angle  have  you  found  in  this  way? 


65]  STUDY  OF  A  MOTOR  AND   DYNAMO  MACHINE.  13$ 


65.     STUDY  OF  A  MOTOR  AND  DYNAMO-MACHINE. 

APPARATUS:  An  electric  motor  (convertible  into  a 
dynamo);  a  source  of  electricity,  a  voltmeter,  an  ammeter. 

I.  Pass  a  current  in  series  through  the  ammeter  and  the 
motor,  held  fast  so  as  not  to  move.      Connect  the  terminals 
through  the  voltmeter  as  a  shunt.      Calculate  the  resistance 
of  the  motor  by  Ohm's  law. 

II.  Find  as  in  I.  the  resistance  of  the  field  magnet  coils. 

III.  Find  as  in  I.  the  resistance  of  the  armature  coils. 

IV.  Repeat  I.  II.  and  III.  with  the  armature  in  motion. 
Is  the  resistance  of  the  armature  apparently  greater  or  less 
than  before?    How  is  this  with  the  field  magnets?    Explain 
these  phenomena  by  the  supposition  that  the   resistances 
are  really  constant,  and  that  the  electromotive  force  varies. 

Under  what  circumstances  can  Ohm's  law  be  applied  to 
the  parts  of  an  electric  motor? 

V.  Find  the  effect  of  forcibly  reversing  the  motor  while 
traversed  by  the  current,  with  the  connections  as  in  III. 

What  is  the  effect  of  doing  work  upon  a  current  upon  its 
magnitude  and  electromotive  force? 

What  is  the  effect  upon  a  current  of  allowing  it  to  do 
work  against  outside  forces? 

Must  work  be  done  upon  or  by  a  current  in  order  that 
the  current  may  be  strengthened? 

VI.  Disconnect  the  voltmeter,  but  leave  the  ammeter  in 
the  main  circuit,  NEXT  TO  THE  ARMATURE  of  the  motor.     Start 
the  motor  by  means  of  the  current. 

Force  the  needle  of  the  ammeter  back  to  zero  by  a  small 
block  touching  it  only  on  one  side,  so  as  to  leave  it  free  to 
respond  to  a  current  in  the  OPPOSITE  direction.  Then  sud- 


134  STUDX   OF  A  MOTOR  AND  DYNAMO  MACHINE.  [65 

denly  shunt  out  the  ammeter  and  the  armature  by  a  short 
thick  wire. 

What  evidence  have  you  that  the  current  induced  in  the 
armature  by  the  motion  of  its  wires  through  the  magnetic 
field  of  the  fixed  or  "field"  magnets  is  opposite  in  direction 
to  that  by  which  the  motion  in  question  is  produced? 

Is  the  armature  accelerated  or  retarded  by  joining  its 
terminals  together,  and  why? 

Note  that  this  experiment  affords  an  excellent  illustration 
of  LENZ'S  LAW. 

VII.  For  this  experiment,  the  connections  may  be  left 
as  in  VI.,  or  still  better,  the  armature  and  ammeter  may  be 
formed  into  a  separate  circuit,  leaving  the  field  magnets 
alone  in  the  main  circuit  with  the  source  of  electricity. 

Find  the  magnitude  of  the  current  induced  in  the 
armature  when  forced  by  mechanical  means  to  rotate  as 
rapidly  as  possible  first  in  one,  then  in  the  opposite 
direction. 

Are  these  induced  currents  in  the  same  or  in  opposite 
directions  ? 

Which  way  must  the  armature  be  made  to  revolve  in 
order  that  the  induced  current  may  strengthen  the  main 
current? 

Give  some  idea  of  the  rate  of  revolution  necessary  to  pro- 
duce a  current  sufficient  to  maintain  the  field  magnets. 

How  would  you  convert  your  motor  into  a  dynamo- 
machine  ? 


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